Skip to content

A Collection of Fractional Calculus Books

A Collection of Fractional Calculus Books

(Last updated: 08/30/2021, 1/25/2022)

(Download the PDF file. 2022 PDF. Please send an email to suggest a missing entry. Thank you!)

2022

  1. H. Singh, H. M. Srivastava, J. J. Nieto. Handbook of Fractional Calculus for Engineering and Science. Chapman and Hall/CRC, 2022. (https://www.amazon.com/Handbook-Fractional-Calculus-Engineering-Mathematics/dp/1032047798/ref=sr_1_25?crid=1631JTEZ7XV23&keywords=Fractional&qid=1642921351&s=books&sprefix=fractional+%2Cstripbooks-intl-ship%2C346&sr=1-25 )
  2. B. Zhang and X. Shu. Fractional-Order Electrical Circuit Theory. Springer Nature, 202 (https://link.springer.com/content/pdf/10.1007/978-981-16-2822-1.pdf )
  3. G. A. Anastassiou. Unification of Fractional Calculi with Applications. Springer Nature, 2022. (https://link.springer.com/content/pdf/10.1007/978-3-030-86920-5.pdf )
  4. J. Wang, S. Liu, and M. Fečkan. Iterative Learning Control for Equations with Fractional Derivatives and Impulses. Springer, 2022. (https://scholar.ustc.cf/extdomains/books.google.com/books?hl=zh-CN&lr=&id=wkpUEAAAQBAJ&oi=fnd&pg=PR5&dq=Iterative+Learning+Control+for+Equations+with+Fractional+Derivatives+and+Impulses&ots=QVOpeaZXaX&sig=io3VJcOZyuOA9369TbFddslvjzQ )

 

 

2021

  1. T. Inoue. The advanced theory of fractional calculus, Third edition. Academic Research Publication, 2021. (https://www.amazon.com/advanced-theory-fractional-calculus-Third-ebook/dp/B09MQ2Q3MS/ref=sr_1_43?crid=1631JTEZ7XV23&keywords=Fractional&qid=1642921362&s=books&sprefix=fractional+%2Cstripbooks-intl-ship%2C346&sr=1-43 )
  2. A. G. Radwan, F. A. Khanday, L. A. Said. Fractional-Order Design: Devices, Circuits, and Systems. Academic Press, 2021. (https://www.goldenlabbookshop.com/book/9780323900904 )
  3. A. G. Radwan, F. A. Khanday, L. A. Said. Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control. Academic Press, 2021. (http://www.lavoisier.eu/books/mechanical-engineering/fractional-order-modeling-of-dynamic-systems-with-applications-in-optimization-signal-processing-and-control/description_4540479 )
  4. P. N. Pathak. Study of generalized functions and their applications. LAP LAMBERT Academic Publishing, 2021. (https://shodhganga.inflibnet.ac.in/handle/10603/261113 )
  5. M. Osman, Z. Gong, and A. M. Mustafa. A Fuzzy Solutions of Fractional-Integer Partial Differential Equations. LAP LAMBERT Academic Publishing, 2021. (https://www.lap-publishing.com/catalog/details//store/gb/book/978-620-3-92821-1/a-fuzzy-solutions-of-fractional-integer-partial-differential-equations )
  6. F. A. Rihan. Delay differential equations and applications to biology. Springer, 2021. (https://link.springer.com/content/pdf/1007/978-981-16-0626-7.pdf )
  7. F. Hamasalh. Spline Algorithm for Solving Fractional Differential Equations. LAP LAMBERT Academic Publishing, 2021.
  8. B. Ahmad and S. K. Ntouyas. Nonlocal Nonlinear Fractional-order Boundary Value Problems. World Scientific, 2021.
  9. B. Ahmad, J. Henderson, and R. Luca. Boundary Value Problems for Fractional Differential Equations and Systems. World Scientific, 2021.
  10. V. Ambrosio. Nonlinear Fractional Schrödinger Equations in R^N. Springer, 2021.
  11. G. A. Anastassiou. Constructive Fractional Analysis with Applications. Springer Nature, 2021.
  12. G. A. Anastassiou. Generalized Fractional Calculus: New Advancements and Applications. Springer, 2021.
  13. A. Atangana and S. I. Araz. New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications. Academic Press, 2021.
  14. B. Jin. Fractional Differential Equations: An Approach via Fractional Derivatives. Springer Nature, 2021.
  15. T. Kaczorek and K. Borawski. Descriptor Systems of Integer and Fractional Orders. Springer Nature, 2021.
  16. M. Li. Theory of Fractional Engineering Vibrations. De Gruyter, 2021.
  17. H. Matthew. Fractional Differential Equations: Numerical Methods for Applications. Springer, 20
  18. H. Singh, J. Singh, S. D. Purohit, and D. Kumar. Advanced Numerical Methods for Differential Equations: Applications in Science and Engineering. CRC Press, 2021.
  19. S. Shao, M. Chen, and P. Shi. Robust Discrete-Time Flight Control of UAV with External Disturbances. Springer, 2021.
  20. V. E. Tarasov and V. V. Tarasova. Economic Dynamics with Memory: Fractional Calculus Approach. Walter de Gruyter GmbH & Co KG, 2021.
  21. E. Tlelo-Cuautle, L. G. De La Fraga, and O. Guillén-Fernández. Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and Their Electronic Realization. CRC Press, 2021.
  22. Z. Trzaska. Mixed Mode Oscillations (MMOs): Fundamentals and Applications. Springer Nature, 2021.

 

2020

  1. T. Allahviranloo. Fuzzy Fractional Differential Operators and Equations: Fuzzy Fractional Differential Equations (Studies in Fuzziness and Soft Computing (397)). Springer, 2020, 305 pages, ISBN-10: 3030512711.
  2. T. Allahviranloo and W. Pedrycz. Soft Numerical Computing in Uncertain Dynamic Systems. Academic Press, 2020.
  3. G. A. Anastassiou. Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Springer, 2020.
  4. K. Bingi, R. Ibrahim, M. N. Karsiti, S. M. Hassan, and V. R. Harindran. Fractional-order Systems and PID Controllers. Springer International Publishing, 2020.
  5. S. Chakraverty, R. M. Jena, and S. K. Jena. Time-fractional Order Biological Systems with Uncertain Parameters. Synthesis Lectures on Mathematics and Statistics. Morgan & Claypool, 2020.
  6. C. Copot, C. M. Ionescu, and C. I. Muresan. Image-Based and Fractional-Order Control for Mechatronic Systems: Theory and Applications with MATLAB®. Springer Nature, 2020.
  7. S. Das. Kindergarten of fractional calculus. Cambridge Scholars Publishing, 2020, 533 pages, ISBN-10: 1527544982.
  8. D. DEEPANJAN and K. B. RASAJIT. Fractional Calculus – Application to Physical Problems. LAP LAMBERT Academic Publishing, 2020.
  9. H. Dutta. Mathematical Methods in Engineering and Applied Sciences. CRC Press, 2020. (https://scholar.ustc.cf/extdomains/books.google.com/books?hl=zh-CN&lr=&id=smjIDwAAQBAJ&oi=fnd&pg=PP1&dq=Mathematical+Methods+in+Engineering+and+Applied+Sciences&ots=FzdHfksvww&sig=Hj2briV5KOK_abyaUL3izTVWnhc )
  10. H. Dutta. Mathematical Modelling in Health, Social and Applied Sciences. Springer Nature, 2020.
  11. H. Dutta, A. O. Akdemir, and A. Atangana. Fractional Order Analysis: Theory, Methods and Applications. Wiley; 2020, 336 pages. ISBN 9781119654162. URL: https://books.google.com/books?id=DEzzDwAAQBAJ.
  12. P. W. Egolf and K. Kutter. Nonlinear, Nonlocal and Fractional Turbulence. Springer, 2020.
  13. CG. Gal and M. Warma. Fractional-in-time Semilinear Parabolic Equations and Applications. Springer, 2020.
  14. BI. Halperin and JK. Jain. Fractional Quantum Hall Effects: New Developments. World Scientific, 2020, 552 pages, ISBN-10: 9811217483.
  15. M. S. Hashemi and D. Baleanu. Lie Symmetry Analysis of Fractional Differential Equations. CRC Press, 2020, 222 pages, ISBN-10: 0367441861.
  16. S. Iqbal, J. Pečarić, and Z. Tomovski. Analytical Inequalities in Fractional Calculus: Hardy, Opial and Related Inequalities. LAP LAMBERT Academic Publishing, 2020.
  17. A. Kubica, K. Ryszewska and M. Yamamoto. Time-Fractional Differential Equations: A Theoretical Introduction. Springer, 2020.
  18. D. Kumar and J. Singh. Fractional Calculus in Medical and Health Science (Mathematics and its Applications). CRC Press, 2020, 264 pages, ISBN-10: 0367351218.
  19. P. Kunche and N. Manikanthababu. Fractional Fourier Transform Techniques for Speech Enhancement. Springer International Publishing AG, 2020.
  20. J. A. T. Machado, N. Özdemir, and D. Baleanu. Numerical Solutions of Realistic Nonlinear Phenomena. Springer Nature, 2020.
  21. R. Martínez-Guerra, F. Meléndez-Vázquez, and I. Trejo-Zúñiga. Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems: Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications. Springer Nature, 2020.
  22. AE. Matouk. Advanced Applications of Fractional Differential Operators to Science and Technology. IGI Global, 2020.
  23. J. Mishra, R. Agarwal, and A. Atangana. Mathematical Modeling and Soft Computing in Epidemiology. CRC Press, 2020.
  24. U. Oberst, M. Scheicher, and I. Scheicher. Linear Time-Invariant Systems, Behaviors and Modules. Springer International Publishing, 2020.
  25. MD. Ortigueira and D. Valério. Fractional Signals and Systems. Walter de Gruyter GmbH & Co KG, 2020.
  26. G. E. Paredes. Fractional-Order Models for Nuclear Reactor Analysis. Woodhead Publishing, 2020.
  27. S. Ray. Nonlinear Differential Equations in Physics. Springer Singapore, 2020.
  28. AP. Singh, D. Deb, H. Agrawal and VE. Balas. Fractional Modeling and Controller Design of Robotic Manipulators: With Hardware Validation. Springer Nature, 2020.
  29. E. Shishkina and S. Sitnik. Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics. Academic Press, 2020.
  30. R. T. Shwayaa. Fractional Integral Differential Equations: Numerical Methods for Solving Fractional Integral Differential Equations. Scholars' Press, 2020.
  31. A. S. Srinivasa Rao and P. Mallikarjuna Rao. Design and Study of Antenna Beam Forming: A Novel Antenna Beam-Forming Concept using Fractional Fourier Transform. Scholars' Press, 2020.
  32. N. Su. Fractional Calculus for Hydrology, Soil Science and Geomechanics: An Introduction to Applications. CRC Press, 2020, 340 pages, ISBN-10: 1138491667.
  33. ZZ. Sun and G. Gao. Fractional Differential Equations: Finite Difference Methods. Walter de Gruyter GmbH & Co KG, 2020, 430 pages, ISBN-10: 3110615177.
  34. E. Tlelo-Cuautle and A. D. Pano-Azucena. Analog/digital Implementation of Fractional Order Chaotic Circuits and Applications. Berlin, Germany: Springer, 2020.
  35. XJ. Yang, F. Gao, and Y. Ju. General Fractional Derivatives with Applications in Viscoelasticity. Academic Press, 2020.

 

2019

  1. R. Almeida, D. Tavares, and DFM. Torres. The Variable-order Fractional Calculus of Variations. Springer International Publishing, 2019.
  2. O. Banna, Y. Mishura, and K. Ralchenko. Fractional Brownian Motion (Approximations of fBm): Weak and Strong Approximations and Projections. Wiley-ISTE, 2019, ISBN-10: 1786302608. https://doi.org/10.1002/9781119476771
  3. R. G. Campos. The XFT Quadrature in Discrete Fourier Analysis. Springer International Publishing, 2019.
  4. A. Carbotti, S. Dipierro, and E. Valdinoci. Local Density of Solutions to Fractional Equations. Walter de Gruyter GmbH & Co KG, 2019, 143 pages, ISBN-10           : 3110660695.
  5. W. Chen, Y. Li, and P. Ma. The Fractional Laplacian. World Scientific Pub Co Inc, 2019, 350 pages, ISBN-10: 9813223995. https://doi.org/10.1142/10550
  6. F. Colombo and J. Gantner. Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion vaes (Operator Theory: Advances and Applications). Birkhäuser, 2019, ISBN-10: 303016408X. https://www.amazon.com/Quaternionic-Operators-Fractional-Diffusion-Processes/dp/303016408X/ref=sr_1_fkmr0_1?keywords=Colombo%2C+J.+Gantner%3A+Quaternionic+Closed+Operators%2C+Fractional+Powers+and+Fractional+Diffusion+Processes+%28Operator+Theory%3A+Advances+and+Applications%29.&qid=1554784917&s=gateway&sr=8-1-fkmr0
  7. J. F. Gómez, L. Torres, and R. F. Escobar. Fractional Derivatives with Mittag-Leffler Kernel: Trends and Applications in Science and Engineering. Springer, 2019, 341 pages, ISBN-10: 3030116611. https://doi.org/10.1007/978-3-030-11662-0
  8. A. Kochubei and Y. Luchko. Fractional Differential Equations (De Gruyter Reference). De Gruyter, 2019, 601 pages, ISBN-10: 3110570823. https://doi.org/10.1515/9783110571660
  9. C. Li and M. Cai. Theory and Numerical Approximations of Fractional Integrals and Derivatives. SIAM, 2019, 312 pages, ISBN: 978-1-61197-587-1, https://doi.org/10.1137/1.9781611975888
  10. Y. Liang, W. Chen, and W. Cai. Hausdorff Calculus: Applications to Fractal Systems (Fractional Calculus in Applied Sciences and Engineering). De Gruyter, 2019, 310 pages, ISBN-10: 3110606925. https://doi.org/10.1515/9783110608526
  11. A. M. Mathai and H. J. Haubold. An Introduction to Fractional Calculus (Mathematics Research Developments). Nova Science Pub Inc, 2019, 258 pages, ISBN-10: 1536146323.

https://books.google.com/books?id=PbGYswEACAAJ&dq=Mathai,+H.+J.+Haubold:+An+Introduction+to+Fractional+Calculus+(Mathematics+Research+Developments).&hl=zh-CN&sa=X&ved=0ahUKEwiRhPv1l8LhAhVUIqYKHVcFAgEQ6AEIKTAA

  1. T. Michelitsch, B. Colle, and A. P. Riascos. Fractional Dynamics on Lattices and Networks. Wiley-ISTE, 2019, 200 pages, ISBN-10: 178630158X.  https://doi.org/10.1002/9781119608165
  2. C. Milici, G. Drăgănescu, and J. T. Machado. Introduction to Fractional Differential Equations (Nonlinear Systems and Complexity). Springer, 2019, 201 pages, ISBN-10: 3030008940.  https://doi.org/10.1007/978-3-030-00895-6
  3. E. C. Oliveira. Solved Exercises in Fractional Calculus (Studies in Systems, Decision and Control). Springer International Publishing, 2019, 340 pages, ISBN-10: 3030205266.
  4. K. M. Owolabi and A. Atangana. Numerical Methods for Fractional Differentiation. Springer Singapore, 2019, 328 pages, ISBN-10: 9811500975.
  5. A. I. Saichev. Distributions in the Physical and Engineering Sciences, Volume 3: Random and Anomalous Fractional Dynamics in Continuous Media. Birkhäuser, 2019, 424 pages, ISBN-10: 3030064670. https://doi.org/10.1007/978-3-319-92586-8
  6. T. Sandev and Ž. Tomovski. Fractional Equations and Models: Theory and Applications. Springer Nature, 2019, 345 pages, ISBN-10: 303029613X.
  7. H. Singh, D. Kumar, and D. Baleanu. Methods of Mathematical Modelling: Fractional Differential Equations. CRC Press, 2019, 254 pages, ISBN-10: 0367220083.
  8. H. M. Srivastava. Operators of Fractional Calculus and Their Applications. MDPI AG, 2019, 136 pages, ISBN-10: 3038973408. https://doi.org/10.3390/math6090157
  9. N. Su. Fractional Calculus in Soil Hydrology and Mechanics: Fundamentals and Applications. CRC Press, 2019, 300 pages, ISBN-10: 1138491667.

https://www.amazon.com/Fractional-Calculus-Soil-Hydrology-Mechanics/dp/1138491667/ref=sr_1_fkmrnull_1?keywords=Fractional+Calculus+in+Soil+Hydrology+and+Mechanics%3A+Fundamentals+and+Applications.&qid=1554784981&s=gateway&sr=8-1-fkmrnull

  1. J. C. Trigeassou and N. Maamri. Analysis, Modeling and Stability of Fractional Order Differential Systems 2: The Infinite State Approach. John Wiley & Sons, 2019, 413 pages, ISBN-10: 1786304554.
  2. Y. Yang and H. H. Zhang. Fractional Calculus with its Applications in Engineering and Technology. Morgan & Claypool, 2019, 109 pages, ISBN: 9781681735160.
  3. XJ. Yang. General Fractional Derivatives: Theory, Methods and Applications. Chapman and Hall/CRC, 2019, 384 pages, ISBN-10: 1138336165.

https://www.amazon.com/General-Fractional-Derivatives-Methods-Applications/dp/1138336165/ref=sr_1_fkmr0_1?keywords=Yang%3A+General+Fractional+Derivatives%3A+Theory%2C+Methods+and+Applications.+C&qid=1554784846&s=gateway&sr=8-1-fkmr0

 

2018

  1. A. Amenta and P. Auscher. Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach. American Mathematical Soc., 2018, 152 pages, ISBN-10: 1470442507. https://doi.org/10.1090/crmm/037
  2. G A. Anastassiou. Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations. Heidelberg: Springer, 2018, 319 pages, ISBN: 978-3-319-66936-6.
  3. G. A. Anastassiou. Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators. Springer, 2018, 293 pages, ISBN-10: 33198950 https://doi.org/10.1007/978-3-319-89509-3
  4. G. A. Anastassiou. Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators. Springer, 2018, 347 pages, ISBN-10: 3030042863. https://doi.org/10.1007/978-3-030-04287-5
  5. G. A. Anastassiou and I. K. Argyros. Functional Numerical Methods: Applications to Abstract Fractional Calculus. Springer, 2018, 161 pages, ISBN-10: 3319887947. https://doi.org/10.1007/978-3-319-69526-6
  6. S. Bhalekar. Frontiers in Fractional Calculus (Current Developments in Mathematical Sciences). Bentham Science Publishers, 2018, 375 pages, ISBN-10: 168108600X. https://doi.org/10.2174/97816810859991180101
  7. K. Cao and Y. Chen. Fractional Order Crowd Dynamics: Cyber-Human System Modeling and Control. Vol. 4. Walter de Gruyter GmbH & Co KG, 2018, 138 pages, ISBN-13: 978-3110472813. https://doi.org/10.1515/9783110473988
  8. S. K. Damarla and M. Kundu. Fractional Order Processes: Simulation, Identification, and Control. CRC Press, 2018, 364 pages, ISBN-10: 0367571137.
  9. J. Dix. Fractional Calculus, Paths on Networks, Geometry, Gravitation: Collected Essays, Volume I. Independently Published, 2018, 109 pages, ISBN-10: 1719825270.

https://books.google.com/books?id=94_9uwEACAAJ&dq=Dix:+Fractional+Calculus,+Paths+on+Networks,+Geometry,+Gravitation:+Collected+Essays,+Volume+I.&hl=zh-CN&sa=X&ved=0ahUKEwjE3MDolcLhAhVE-WEKHT-WAS0Q6AEIKTAA

  1. M. Edelman, E. N. Macau, and M. Sanjuan. Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Springer, 2018, 315 pages, ISBN-10: 3319681087. https://doi.org/10.1007/978-3-319-68109-2
  2. L. R. Evangelista and E. K. Lenzi. Fractional Diffusion Equations and Anomalous Diffusion. Cambridge University Press, 2018, 358 pages, ISBN-10: 9781107143555. https://doi.org/10.1017/9781316534649
  3. F. Ge, Y. Chen, and C. Kou. Regional Analysis of Time-fractional Diffusion Processes. Springer International Publishing, 2018, 250 pages, ISBN-10: 9783319728957. https://doi.org/10.1007/978-3-319-72896-4
  4. S. G. Georgiev. Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales. Springer, 2018, 360 pages, ISBN-10: 9783319739533. https://doi.org/10.1007/978-3-319-73954-0
  5. H. J. Hans. Special Functions: Fractional Calculus and the Pathway for Entropy. MDPI, 2018, 304 pages, ISBN-10: 3038426652. https://doi.org/10.3390/books978-3-03842-664-6
  6. C. F. Lorenzo and T. Hartley. Generalized Functions for the Fractional Calculus. Independently published, 1999 (2018 Publish), 36pages, ISBN-10: 1724034332. https://doi.org/10.1615/critrevbiomedeng.v36.i1.40
  7. R. Martínez-Guerra and C. A. Pérez-Pinacho. Advances in Synchronization of Coupled Fractional Order Systems: Fundamentals and Methods. Springer, 2018, 185 pages, ISBN-10: 3319939459, ISBN-13: 978-3319939452. https://doi.org/10.1007/978-3-319-93946-9
  8. C. Skiadas. Fractional Dynamics, Anomalous Transport and Plasma Science. Springer, 2018, 201 pages, ISBN-10: 3030044823. https://doi.org/10.1007/978-3-030-04483-1
  9. V. Vyawahare and P. V. Nataraj. Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models: A Systematic Approach. Springer, 2018, 200 pages, ISBN-10: 9811356556. https://doi.org/10.1007/978-981-10-7587-2

 

2017

  1. A. T. Azar, S. Vaidyanathan, and A. Ouannas. Fractional Order Control and Synchronization of Chaotic Systems. Springer, 2017, 877 pages, ISBN-10: 3319502484. https://doi.org/10.1007/978-3-319-50249-6
  2. M. Chen, S. Shao, and P. Shi. Robust Adaptive Control for Fractional-order Systems with Disturbance and Saturation. Wiley-ASME Press Series, 2017, 256 pages, ISBN-10: 1119393272. https://doi.org/10.1002/9781119393351
  3. M. Fečkan, J. Wang, and M. Pospíšil. Fractional-order Equations and Inclusions. Walter de Gruyter GmbH & Co KG, 2017, 367 pages, ISBN-10: 3110521385, ISBN-13: 978-3110521382. https://doi.org/10.1515/9783110522075
  4. K. Kubilius, Y. Mishura, and K. Ralchenko. Parameter Estimation in Fractional Diffusion Models. Springer, 2017, 390 pages, ISBN-10: 331971029X. https://doi.org/10.1007/978-3-319-71030-3
  5. A. M. Mathai and H. J. Haubold. Fractional and Multivariable Calculus: Model Building and Optimization Problems. Springer, 2017, 234 pages, ISBN-10: 3319599925. https://doi.org/10.1007/978-3-319-59993-9
  6. I. M. Stamova and G. T. Stamov. Functional and Impulsive Differential Equations of Fractional Order: Qualitative Analysis and Applications. CRC Press, 2017, 276 pages, ISBN-10: 1498764835. https://doi.org/10.1201/9781315367453
  7. R. U. Verma. Semi-Infinite Fractional Programming. Springer Singapore, 2017, 291 pages, ISBN-10: 9811062552. https://doi.org/10.1007/978-981-10-6256-8_4
  8. B. J. West. Nature’s Patterns and the Fractional Calculus. Walter de Gruyter GmbH & Co KG, 2017, 199 pages, ISBN-10: 3110534118, ISBN-13: 978-3110534115. https://doi.org/10.1515/9783110535136
  9. D. Xue. Fractional-order Control Systems: Fundamentals and Numerical Implementations. Vol. 1. Walter de Gruyter GmbH & Co KG, 2017, 320 pages, ISBN-10: 3110499991. https://doi.org/10.1515/9783110497977

 

2016

  1. G. A. Anastassiou and I. K. Argyros. Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus. Springer International Publishing, 2016, 116 pages, ISBN-10: 3319336053. https://doi.org/10.1007/978-3-319-33606-0
  2. S. Chakraverty, S. Tapaswini, and D. Behera. Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications. John Wiley & Sons, 2016, 272 pages, ISBN-10: 111900411X. https://doi.org/10.1002/9781119004233
  3. C. F. Lorenzo and T. T. Hartley. The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science. John Wiley & Sons, 2016, 464 pages, ISBN-10: 9781119139409. https://doi.org/10.1002/9781119139447
  4. C. Pozrikidis. The Fractional Laplacian. Chapman and Hall/CRC, 2016, 294 pages, ISBN-10: 1498746152. https://doi.org/10.1201/b19666
  5. B. J. West. Fractional Calculus View of Complexity: Tomorrow’s Science. CRC Press, 2016, 285 pages, ISBN-13: 978-1-4987-3800-2. https://doi.org/10.1201/b18911

 

2015

  1. B. Bandyopadhyay and S. Kamal. Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach. Vol. 317. Switzerland: Springer International Publishing, 2015, 200 pages, ISBN-10: 3319086200.  https://doi.org/10.1007/978-3-319-08621-7
  2. T. Kaczorek and K. Rogowski. Fractional Linear Systems and Electrical Circuits (Studies in Systems, Decision and Control). Cham, Switzerland: Springer International Publishing, 2015, 254 pages, ISBN-10: 3319113607. https://doi.org/10.1007/978-3-319-11361-6
  3. C. Li and F. Zeng. Numerical Methods for Fractional Calculus. Chapman and Hall/CRC, 2015, 300 pages, ISBN-10: 1482253801. https://doi.org/10.1201/b18503
  4. A. B. Malinowska, T. Odzijewicz, and F. M. Torres. Advanced Methods in the Fractional Calculus of Al. Springer, 2015, 148 pages, ISBN-10: 9783319147550. https://doi.org/10.1007/978-3-319-14756-7
  5. R. Martínez-Guerra, C. A. Pérez-Pinacho, and G. C. Gómez-Cortés. Synchronization of Integral and Fractional Order Chaotic Systems: A Differential Algebraic and Differential Geometric Approach. Springer, 2015, 242 pages, ISBN-10: 3319152831. https://www.springer.com/gp/book/9783319152837
  6. F. Padula and A. Visioli. Advances in Robust Fractional Control. Chum, Switzerland: Springer, 2015, 176 pages, ISBN-10: 3319109294. https://doi.org/10.1007/978-3-319-10930-5
  7. Y. Povstenko. Fractional Thermoelasticity (Solid Mechanics and Its Applications). Springer, 2015, 253 pages, ISBN-10: 331915334X. https://doi.org/10.1007/978-3-319-15335-3

 

2014

  1. T. M. Atanackovic. Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes. John Wiley & Sons, 2014, 336 pages, ISBN-10: 9781848214170. https://doi.org/10.1002/9781118577530
  2. R. Herrmann. Fractional Calculus: An Introduction for Physicists (2nd Edition). World Scientific, 2014, 500 pages, ISBN-10: 9814551074.  https://doi.org/10.1142/9789814551083_0005
  3. R. Gorenflo, A A Kilbas, F. Mainardi, and SV. Rogosin. Mittag-Leffler Functions, Related Topics and Applications. Springer, 2014, 443 pages, ISBN-10: 3662439298.

 

2013

  1. S. Cohen and J. Istas. Fractional Fields and Applications. Springer, 2013, 284 pages, ISBN-10: 3642367380. https://doi.org/10.1007/978-3-642-36739-7
  2. V. Daftardar-Gejji. Fractional Calculus: Theory and Applications. Narosa, New Delhi, 2013, 232 pages, ISBN-10: 8184873336. https://books.google.com/books?id=fBWYngEACAAJ&dq=Fractional+Calculus:+Theory+and+Applications.&hl=zh-CN&sa=X&ved=0ahUKEwj7uc6cksLhAhUOQN4KHaLXAzUQ6AEIMDAB

 

2012

  1. G. Amendola, M. Fabrizio, and JM. Golden. Thermodynamics of Materials with Memory: Theory and Applications. Springer. 2012. (https://link.springer.com/book/10.1007/978-1-4614-1692-0 )
  2. S. Abbas, M. Benchohra and G. M. N'Guérékata. Topics in Fractional Differential Equations. Springer Science & Business Media, 2012, 412 pages, ISBN-10: 1489995471.

https://books.google.com/books?hl=zh-CN&lr=&id=UCkQAN3teM4C&oi=fnd&pg=PR7&dq=Topics+in+fractional+differential+equations.+&ots=S8XYK8mmqu&sig=BaBgT97fLqae5CPkmkWZBo5Yf6A

  1. M. H. Annaby and Z. S. Mansour. Q-fractional Calculus and Equations. Springer, 2012, 340 pages, ISBN-10: 364230897X.

https://books.google.com/books?hl=zh-CN&lr=&id=OEi5BQAAQBAJ&oi=fnd&pg=PR3&dq=Q-fractional+Calculus+and+Equations&ots=GEf146VQaQ&sig=bUVEjU8JRQ4IBYKY4DQxra4bFEs

  1. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo.  Fractional Calculus: Models and Numerical Methods. World Scientific, 2012, 428 pages, ISBN-10: 981-4355-20-8, ISBN-13: 978-981-4355-20-9. (2nd Edition, 2016, 478 pages, ISBN-10: 9813140038, ISBN-13: 978-9813140035.)

https://books.google.com/books?hl=zh-CN&lr=&id=NhS7CgAAQBAJ&oi=fnd&pg=PR7&dq=Fractional+calculus:+models+and+numerical+methods.&ots=JIdFMsnz50&sig=yd1pgI9uZLorKz0NI3dzDWg1Xu8

  1. D. Baleanu, J. A. Machado, and A. Luo. Fractional Dynamics and Control. Springer Science & Business Media, 2012, 309 pages, ISBN-13: 978-1-4614-0456-9.

https://books.google.com/books?hl=zh-CN&lr=&id=8tpLwiLONDkC&oi=fnd&pg=PR1&dq=Fractional+dynamics+and+control&ots=fwX4VBw2tj&sig=G8mvORy4ULXev3UKqcsx_KMAh2Q

  1. J. Klafter, S. C. Lim, and R. Metzler. Fractional Dynamics: Recent Advances. World Scientific, 2012, 530 pages, ISBN-13: 978-981-4340-58-8. https://doi.org/10.1142/8087
  2. Y. Luo and Y. Chen. Fractional Order Motion Controls. John Wiley & Sons, 2012, 454 pages, ISBN-10: 1119944554. https://doi.org/10.1002/9781118387726
  3. I. Nourdin. Selected Aspects of Fractional Brownian Motion. Springer, 2012, 122 pages, ISBN-10: 8847028221. https://doi.org/10.1007/978-88-470-2823-4
  4. I. Pan and S. Das. Intelligent Fractional Order Systems and Control: An Introduction. Springer, 2012, 316 pages, ISBN-10: 3642438520.

https://books.google.com/books?hl=zh-CN&lr=&id=bLy5BQAAQBAJ&oi=fnd&pg=PR3&dq=Intelligent+fractional+order+systems+and+control:+an+introduction.&ots=ZchTWQmTVc&sig=F-z6ez_Th4bXStFBpYRW-NVnuZI

  1. M. Zubair, M. J. Mughal, and Q. A. Naqvi. Electromagnetic Fields and Waves in Fractional Dimensional Space. Springer Science & Business Media, 2012, 88 pages, ISBN-10: 3642253571. https://doi.org/10.1007/978-3-642-25358-4

 

2011

  1. S. Das and I. Pan. Fractional Order Signal Processing: Introductory Concepts and Applications. Springer Science & Business Media, 2011, 116 pages, ISBN-10: 3642231160.

https://books.google.com/books?hl=zh-CN&lr=&id=qHKQ92q1uRIC&oi=fnd&pg=PP3&dq=Fractional+order+signal+processing:+introductory+concepts+and+applications.+&ots=wQmdtYyOaE&sig=1emlJZamePtOgZ6RR1XFLwhet7Q

  1. S. Das. Functional Fractional Calculus. Springer Science & Business Media, 2011, 612 pages, ISBN-10: 3642205445. https://doi.org/10.1007/978-3-642-20545-3
  2. T. Kaczorek. Selected Problems of Fractional Systems Theory. Springer Science & Business Media, 2011, 364 pages, ISBN-10: 3642205011. https://doi.org/10.1007/978-3-642-20502-6
  3. J. S. Leszczyński. An Introduction to Fractional Mechanics. Publishing Office of Czestochowa University of Technology, 2011, 128 pages, ISBN: 978-83-7193-494-0.

https://books.google.com/books?id=dlFdLwEACAAJ&dq=An+introduction+to+fractional+mechanics&hl=zh-CN&sa=X&ved=0ahUKEwjLro2cj8LhAhUPBKYKHUcPBnwQ6AEIKTAA

  1. M. M. Meerschaert and A. Sikorskii. Stochastic Models for Fractional Calculus. Walter de Gruyter, 2011, 391 pages, ISBN-10: 3110258692, ISBN-13: 978-3-11-025869-1. https://doi.org/10.1515/9783110258165
  2. M. D. Ortigueira. Fractional Calculus for Scientists and Engineers. Springer Science & Business Media, 2011, 154 pages, ISBN-10: 978940070746-7. https://doi.org/10.1007/978-94-007-0747-4
  3. I. Petráš. Fractional-order Nonlinear Systems: Modeling, Analysis and Simulation. Springer Science & Business Media, 2011, 218 pages, ISBN-10: 9783642181009.

https://books.google.com/books?hl=zh-CN&lr=&id=6exW-H3nllUC&oi=fnd&pg=PP4&dq=Fractional-order+nonlinear+systems:+modeling,+analysis+and+simulation&ots=Fgof4sGmIF&sig=1f8klkBBsjI4WjMclBIwiSl-KFI

  1. B. L. S. Prakasa Rao. Statistical Inference for Fractional Diffusion Processes. John Wiley & Sons, 2011, 280 pages, ISBN-10: 0470665688.

https://books.google.com/books?hl=zh-CN&lr=&id=kjFvTEWHmD0C&oi=fnd&pg=PT5&dq=Statistical+inference+for+fractional+diffusion+processes.&ots=O6-AfSsjrI&sig=GsjUTB3hfs9AXaWnvTcA9nVyINU

  1. E. R. Scheinerman and D. H. Ullman. Fractional Graph Theory: A Rational Approach to the Theory of Graphs. Dover Publications, 2011, 240 pages, ISBN-10: 0486485935.

https://books.google.com/books?hl=zh-CN&lr=&id=zzFxD8kPWigC&oi=fnd&pg=PP1&dq=Fractional+graph+theory:+a+rational+approach+to+the+theory+of+graphs.&ots=yUl8wVwQuh&sig=vhnLfwe2PehOVuvj5hMfrtEGuMs

  1. H. Sheng, Y. Chen, and T. Qiu. Fractional Processes and Fractional-order Signal Processing: Techniques and Applications. Springer Science & Business Media, 2011, 295 pages, ISBN-10: 1447122321. https://doi.org/10.1007/978-1-4471-2233-3
  2. V. E. Tarasov. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer Science & Business Media, 2011, 505 pages, ISBN-10: 3642140025.

https://books.google.com/books?hl=zh-CN&lr=&id=Mc193Swt_JQC&oi=fnd&pg=PR3&dq=+Fractional+dynamics:+applications+of+fractional+calculus+to+dynamics+of+particles,+fields+and+media&ots=_gBx4JfWTC&sig=P_MB5FqT9V58h4QckvPsOvXGJbU

 

2010

  1. D. Baleanu, Z. B. Güvenç, and J. A. Tenreiro Machado. New Trends in Nanotechnology and Fractional Calculus Applications. New York: Springer, 2010, 531 pages, ISBN-10: 9048132924.

https://link.springer.com/content/pdf/10.1007/978-90-481-3293-5.pdf

  1. R. Caponetto, G. Dongola, L. Fortuna, and I. Petras. Fractional Order Systems: Modeling and Control Applications. Vol. 72. World Scientific, 2010, 200 pages, ISBN-10: 9814304190. https://doi.org/10.1142/7709
  2. K. Diethelm. The Analysis of Fractional Differential Equations: An Application-oriented Exposition Using Differential Operators of Caputo Type. Springer Science & Business Media, 2010, 264 pages, ISBN-10: 9783642145735.

https://books.google.com/books?hl=zh-CN&lr=&id=K4vKvX98SM8C&oi=fnd&pg=PR5&dq=The+analysis+of+fractional+differential+equations:+An+application-oriented+exposition+using+differential+operators+of+Caputo+type&ots=OLfUngs9qI&sig=R4bv02KvATFWuIWu4n7Jw2AQ91Y

  1. A.C. J. Luo and V. Afraimovich. Long-range Interactions, Stochasticity and Fractional Dynamics: Dedicated to George M. Zaslavsky (1935—2008). Springer Science & Business Media, 2010, 311 pages, ISBN-10: 3642123422. https://doi.org/10.1007/978-3-642-12343-6
  2. F. Mainardi. Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Pr, 2010, 347 pages, ISBN-10: 1848163290. https://doi.org/10.1142/9781848163300
  3. C. A. Monje, Y. Chen, B. M. Vinagre, D Xue, and V Feliu-Batlle. Fractional-order Systems and Controls: Fundamentals and Applications. Springer Science & Business Media, 2010, 415 pages, ISBN-10: 1849963347. https://books.google.com/books?hl=zh-CN&lr=&id=c4fV9WeCiEwC&oi=fnd&pg=PR9&dq=Fractional-order+systems+and+controls:+fundamentals+and+applications&ots=E0qVR5hOOG&sig=doWtdgj9ktit2FL2phtkmRenhaA

 

2009

  1. M. Klimek. On Solutions of Linear Fractional Differential Equations of a Variational Type. Publishing Office of Czestochowa University of Technology, 2009, 244 pages, ISBN-10: 837193422X.

https://www.amazon.com/Solutions-Fractional-Differential-Equations-Variational/dp/837193422X/ref=sr_1_fkmrnull_1?keywords=ISBN-10%3A+837193422X&qid=1554781703&s=gateway&sr=8-1-fkmrnull

  1. S. Rostek. Option Pricing in Fractional Brownian Markets (Lecture Notes in Economics and Mathematical Systems). Springer, 2009, 152 pages, ISBN-10: 3642003303. https://doi.org/10.1007/978-3-642-00331-8

 

2008

  1. F. Biagini, Y. Hu, B Øksendal, and T Zhang. Stochastic Calculus for Fractional Brownian Motion and Applications. Springer Science & Business Media, 2008, 330 pages, ISBN-10: 9781852339968. https://books.google.com/books?hl=zh-CN&lr=&id=ccdwU2NW9f4C&oi=fnd&pg=PR7&dq=Stochastic+calculus+for+fractional+Brownian+motion+and+applications.&ots=b5NOKs6EbL&sig=OV6E3GuDpNHDmGYMBDi4uIdy1No
  2. S. Das. Functional Fractional Calculus for System Identification and Controls. Springer, 2008, 260 pages, ISBN-10: 3642091784. https://doi.org/10.1007/978-3-540-72703-3
  3. Y. Mishura. Stochastic Calculus for Fractional Brownian Motion and Related Processes. Vol. 1929. Springer Science & Business Media, 2008, 416 pages, ISBN-10: 3540758720. https://doi.org/10.1007/978-3-540-75873-0

 

2007

  1. J. Sabatier, O. P. Agrawal, and J. A. Tenreiro Machado. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Vol. 4. No. 9. Dordrecht: Springer, 2007, 552 pages, ISBN-10: 9781402060410. https://www.springer.com/gp/book/9781402060410

 

2006

  1. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo. Theory and Applications of Fractional Differential Equations. Vol. 204. Elsevier Science Limited, 2006, 540 pages, ISBN-10: 0444518320. https://doi.org/10.1016/s0304-0208(06)x8001-5
  2. R. L. Magin. Fractional Calculus in Bioengineering. Redding: Begell House, 2006, 684 pages, ISBN-10: 1567002153. https://www.amazon.com/Fractional-Calculus-Bioengineering-Richard-Magin/dp/1567002153

 

2005

  1. R. A. Hibschweiler and T. H. MacGregor. Fractional Cauchy Transforms. Chapman and Hall/CRC, 2005, 272 pages, ISBN 10: 1584885602. https://doi.org/10.1201/9781420034875
  2. A. Khare. Fractional Statistics and Quantum Theory. World Scientific, 2005, 316 pages, ISBN-10: 9812561609. https://doi.org/10.1142/9789812567758
  3. G. M. Zaslavsky. Hamiltonian Chaos and Fractional Dynamics. Oxford University Press on Demand, 2005, 436 pages, ISBN-10: 0199535485.

https://books.google.com/books?hl=zh-CN&lr=&id=qMQRDAAAQBAJ&oi=fnd&pg=PR9&dq=Hamiltonian+chaos+and+fractional+dynamics&ots=DCujWn5rd6&sig=RcGkUqvW2xt84RpuvILipodLDtI

 

2004

  1. A. M. F. Ohashi. Evolution Equations Driven by a Fractional White Noise in Spaces of Abstract Stochastic Distributions. UNICAMP, 2004, 25 pages. http://143.106.77.95/sites/default/files/rel_pesq/rp44-04.pdf

 

2003

  1. E. B. Bajalinov. Linear-fractional Programming Theory, Methods, Applications and Software. Vol. 84. Springer Science & Business Media, 2003, 425 pages, ISBN-10: 1461348226. https://doi.org/10.1007/978-1-4419-9174-4
  2. B. J. West, M. Bologna, and P. Grigolini. Physics of Fractal Operators. Springer, 2003, 354 pages, ISBN 0-387-95554-2. https://doi.org/10.1063/1.1650234

 

2001

  1. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay. The Fractional Fourier Transform with Applications in Optics and Signal Processing. John Wiley, 2001, 513 pages, ISBN-13: 987-0471963462.

https://ieeexplore.ieee.org/abstract/document/7076127/

 

2000

  1. R. Hilfer. Applications of Fractional Calculus in Physics. World Scientific, 2000, 472 pages, ISBN-10: 9810234570. https://doi.org/10.1142/9789812817747

 

1998

  1. A. I. Barros. Discrete and Fractional Programming Techniques for Location Models. Springer Science & Business Media, 1998, 180 pages, ISBN-10: 1461368243. https://doi.org/10.1007/978-1-4615-4072-4
  2. I. Podlubny. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, 1998, 340 pages, ISBN-10: 0125588402. https://doi.org/10.1016/s0076-5392(99)x8001-5

 

1997

  1. N. K. Bliev. Generalized Analytic Functions in Fractional Spaces. Vol. 86. CRC Press, 1997, 160 pages, ISBN-10: 0582288614.

https://books.google.com/books?hl=zh-CN&lr=&id=TU8X2NpAGXEC&oi=fnd&pg=PP9&dq=Generalized+analytic+functions+in+fractional+spaces&ots=XprTah5HFS&sig=L3PVzRbWkZw3bba146FYczrqg3E

  1. A. Carpinteri and F. Mainardi. Fractals and Fractional Calculus in Continuum Mechanics. Vol. 378. Springer, 1997, 348 pages, ISBN-10: 321182913X. https://doi.org/10.1007/978-3-7091-2664-6
  2. I. V. Novozhilov. Fractional Analysis: Methods of Motion Decomposition. Springer Science & Business Media, 1997, 232 pages, ISBN-10: 1461286670.

https://books.google.com/books?hl=zh-CN&lr=&id=mwHaBwAAQBAJ&oi=fnd&pg=PP8&dq=Fractional+analysis:+Methods+of+motion+decomposition&ots=YXVzeEXwEo&sig=GPRVqNwfwjdSrIDGUGSGJLMAiko

 

1996

  1. B. Rubin. Fractional Integrals and Potentials. Chapman and Hall/CRC, 1996, 424 pages, ISBN-10: 0582253411.

https://books.google.com/books?hl=zh-CN&lr=&id=eN6VHU_mMaoC&oi=fnd&pg=PR11&dq=Fractional+integrals+and+potentials&ots=_pc7PBNwP0&sig=pBZgwte__kV5f3AVyZTuQReOJMI

  1. T. Runst and W. Sickel. Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. Walter de Gruyter, 1996, 560 pages, ISBN: 3-11-015113-8.

https://books.google.com/books?hl=zh-CN&lr=&id=x0-RHMg-8_wC&oi=fnd&pg=PA1&dq=Sobolev+spaces+of+fractional+order,+Nemytskij+operators,+and+nonlinear+partial+differential+equations&ots=0XSFuexCIi&sig=lVZyESCf4UIeSx4gIr_vjP9sK9s

 

1995

  1. T. Chakraborty and P. Pietiläinen. The Quantum Hall Effects: Integral and Fractional. Vol. 85. Springer Science & Business Media, 1995, 302 pages, ISBN-10: 354058515X.

https://books.google.com/books?hl=zh-CN&lr=&id=v5nzCAAAQBAJ&oi=fnd&pg=PA1&dq=The+quantum+Hall+effects:+integral+and+fractional&ots=4SuDoq_4Ud&sig=SPJ_6OOZ9IzJm2sMiPq9vtjTi3s

 

1993

  1. V. S. Kiryakova. Generalized Fractional Calculus and Applications. CRC press, 1993, 360 pages, ISBN-10: 0582219779.

https://books.google.com/books?hl=zh-CN&lr=&id=RvcONCIkFwoC&oi=fnd&pg=PP15&dq=Generalized+fractional+calculus+and+applications&ots=fE4EE7OmF7&sig=Jte-4O4kIcAT5qzzrCH8OP2o4CY

  1. K. S. Miller and B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley-Interscience, 1993, 384 pages, ISBN-10: 0471588849. https://www.amazon.com/Introduction-Fractional-Calculus-Differential-Equations/dp/0471588849
  2. S. G. Samko, A. A. Kilbas, and O. I. Marichev. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, 1993, 1006 pages, ISBN 2881248640.

https://www.amazon.com/Fractional-Integrals-Derivatives-Theory-Applications/dp/2881248640

 

 

1990

  1. F. Wilczek. Fractional Statistics and Anyon Superconductivity. World scientific, 1990, 460 pages, ISBN-10: 9810200498. https://doi.org/10.1142/0961

 

1974

  1. K. B. Oldham and J. Spanier. The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. Dover Publications, 1974, 234 pages, ISBN-10: 0486450015. https://doi.org/10.1016/s0076-5392(09)x6012-1

 

 

 

 

 

 

 

 

 

 

 

Key words: Fractional

Sources: Google Scholar, Amazon Books

The most recent unpublished books for 2022 are not listed.

If there is omission, welcome to add!

Credits: Lihong Guo, YangQuan Chen, Richard L. Magin.

Time: Jan. 23, 2022