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
- 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 )
- 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 )
- 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 )
- 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
- 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 )
- 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 )
- 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 )
- P. N. Pathak. Study of generalized functions and their applications. LAP LAMBERT Academic Publishing, 2021. (https://shodhganga.inflibnet.ac.in/handle/10603/261113 )
- 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 )
- 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 )
- F. Hamasalh. Spline Algorithm for Solving Fractional Differential Equations. LAP LAMBERT Academic Publishing, 2021.
- B. Ahmad and S. K. Ntouyas. Nonlocal Nonlinear Fractional-order Boundary Value Problems. World Scientific, 2021.
- B. Ahmad, J. Henderson, and R. Luca. Boundary Value Problems for Fractional Differential Equations and Systems. World Scientific, 2021.
- V. Ambrosio. Nonlinear Fractional Schrödinger Equations in R^N. Springer, 2021.
- G. A. Anastassiou. Constructive Fractional Analysis with Applications. Springer Nature, 2021.
- G. A. Anastassiou. Generalized Fractional Calculus: New Advancements and Applications. Springer, 2021.
- A. Atangana and S. I. Araz. New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications. Academic Press, 2021.
- B. Jin. Fractional Differential Equations: An Approach via Fractional Derivatives. Springer Nature, 2021.
- T. Kaczorek and K. Borawski. Descriptor Systems of Integer and Fractional Orders. Springer Nature, 2021.
- M. Li. Theory of Fractional Engineering Vibrations. De Gruyter, 2021.
- H. Matthew. Fractional Differential Equations: Numerical Methods for Applications. Springer, 20
- H. Singh, J. Singh, S. D. Purohit, and D. Kumar. Advanced Numerical Methods for Differential Equations: Applications in Science and Engineering. CRC Press, 2021.
- S. Shao, M. Chen, and P. Shi. Robust Discrete-Time Flight Control of UAV with External Disturbances. Springer, 2021.
- V. E. Tarasov and V. V. Tarasova. Economic Dynamics with Memory: Fractional Calculus Approach. Walter de Gruyter GmbH & Co KG, 2021.
- 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.
- Z. Trzaska. Mixed Mode Oscillations (MMOs): Fundamentals and Applications. Springer Nature, 2021.
2020
- 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.
- T. Allahviranloo and W. Pedrycz. Soft Numerical Computing in Uncertain Dynamic Systems. Academic Press, 2020.
- G. A. Anastassiou. Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Springer, 2020.
- K. Bingi, R. Ibrahim, M. N. Karsiti, S. M. Hassan, and V. R. Harindran. Fractional-order Systems and PID Controllers. Springer International Publishing, 2020.
- 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.
- 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.
- S. Das. Kindergarten of fractional calculus. Cambridge Scholars Publishing, 2020, 533 pages, ISBN-10: 1527544982.
- D. DEEPANJAN and K. B. RASAJIT. Fractional Calculus – Application to Physical Problems. LAP LAMBERT Academic Publishing, 2020.
- 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 )
- H. Dutta. Mathematical Modelling in Health, Social and Applied Sciences. Springer Nature, 2020.
- 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.
- P. W. Egolf and K. Kutter. Nonlinear, Nonlocal and Fractional Turbulence. Springer, 2020.
- CG. Gal and M. Warma. Fractional-in-time Semilinear Parabolic Equations and Applications. Springer, 2020.
- BI. Halperin and JK. Jain. Fractional Quantum Hall Effects: New Developments. World Scientific, 2020, 552 pages, ISBN-10: 9811217483.
- M. S. Hashemi and D. Baleanu. Lie Symmetry Analysis of Fractional Differential Equations. CRC Press, 2020, 222 pages, ISBN-10: 0367441861.
- S. Iqbal, J. Pečarić, and Z. Tomovski. Analytical Inequalities in Fractional Calculus: Hardy, Opial and Related Inequalities. LAP LAMBERT Academic Publishing, 2020.
- A. Kubica, K. Ryszewska and M. Yamamoto. Time-Fractional Differential Equations: A Theoretical Introduction. Springer, 2020.
- D. Kumar and J. Singh. Fractional Calculus in Medical and Health Science (Mathematics and its Applications). CRC Press, 2020, 264 pages, ISBN-10: 0367351218.
- P. Kunche and N. Manikanthababu. Fractional Fourier Transform Techniques for Speech Enhancement. Springer International Publishing AG, 2020.
- J. A. T. Machado, N. Özdemir, and D. Baleanu. Numerical Solutions of Realistic Nonlinear Phenomena. Springer Nature, 2020.
- 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.
- AE. Matouk. Advanced Applications of Fractional Differential Operators to Science and Technology. IGI Global, 2020.
- J. Mishra, R. Agarwal, and A. Atangana. Mathematical Modeling and Soft Computing in Epidemiology. CRC Press, 2020.
- U. Oberst, M. Scheicher, and I. Scheicher. Linear Time-Invariant Systems, Behaviors and Modules. Springer International Publishing, 2020.
- MD. Ortigueira and D. Valério. Fractional Signals and Systems. Walter de Gruyter GmbH & Co KG, 2020.
- G. E. Paredes. Fractional-Order Models for Nuclear Reactor Analysis. Woodhead Publishing, 2020.
- S. Ray. Nonlinear Differential Equations in Physics. Springer Singapore, 2020.
- AP. Singh, D. Deb, H. Agrawal and VE. Balas. Fractional Modeling and Controller Design of Robotic Manipulators: With Hardware Validation. Springer Nature, 2020.
- E. Shishkina and S. Sitnik. Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics. Academic Press, 2020.
- R. T. Shwayaa. Fractional Integral Differential Equations: Numerical Methods for Solving Fractional Integral Differential Equations. Scholars' Press, 2020.
- 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.
- N. Su. Fractional Calculus for Hydrology, Soil Science and Geomechanics: An Introduction to Applications. CRC Press, 2020, 340 pages, ISBN-10: 1138491667.
- ZZ. Sun and G. Gao. Fractional Differential Equations: Finite Difference Methods. Walter de Gruyter GmbH & Co KG, 2020, 430 pages, ISBN-10: 3110615177.
- E. Tlelo-Cuautle and A. D. Pano-Azucena. Analog/digital Implementation of Fractional Order Chaotic Circuits and Applications. Berlin, Germany: Springer, 2020.
- XJ. Yang, F. Gao, and Y. Ju. General Fractional Derivatives with Applications in Viscoelasticity. Academic Press, 2020.
2019
- R. Almeida, D. Tavares, and DFM. Torres. The Variable-order Fractional Calculus of Variations. Springer International Publishing, 2019.
- 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
- R. G. Campos. The XFT Quadrature in Discrete Fourier Analysis. Springer International Publishing, 2019.
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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
- 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
- E. C. Oliveira. Solved Exercises in Fractional Calculus (Studies in Systems, Decision and Control). Springer International Publishing, 2019, 340 pages, ISBN-10: 3030205266.
- K. M. Owolabi and A. Atangana. Numerical Methods for Fractional Differentiation. Springer Singapore, 2019, 328 pages, ISBN-10: 9811500975.
- 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
- T. Sandev and Ž. Tomovski. Fractional Equations and Models: Theory and Applications. Springer Nature, 2019, 345 pages, ISBN-10: 303029613X.
- H. Singh, D. Kumar, and D. Baleanu. Methods of Mathematical Modelling: Fractional Differential Equations. CRC Press, 2019, 254 pages, ISBN-10: 0367220083.
- H. M. Srivastava. Operators of Fractional Calculus and Their Applications. MDPI AG, 2019, 136 pages, ISBN-10: 3038973408. https://doi.org/10.3390/math6090157
- N. Su. Fractional Calculus in Soil Hydrology and Mechanics: Fundamentals and Applications. CRC Press, 2019, 300 pages, ISBN-10: 1138491667.
- 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.
- Y. Yang and H. H. Zhang. Fractional Calculus with its Applications in Engineering and Technology. Morgan & Claypool, 2019, 109 pages, ISBN: 9781681735160.
- XJ. Yang. General Fractional Derivatives: Theory, Methods and Applications. Chapman and Hall/CRC, 2019, 384 pages, ISBN-10: 1138336165.
2018
- 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
- G A. Anastassiou. Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations. Heidelberg: Springer, 2018, 319 pages, ISBN: 978-3-319-66936-6.
- 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
- 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
- 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
- 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
- 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
- S. K. Damarla and M. Kundu. Fractional Order Processes: Simulation, Identification, and Control. CRC Press, 2018, 364 pages, ISBN-10: 0367571137.
- J. Dix. Fractional Calculus, Paths on Networks, Geometry, Gravitation: Collected Essays, Volume I. Independently Published, 2018, 109 pages, ISBN-10: 1719825270.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- C. Pozrikidis. The Fractional Laplacian. Chapman and Hall/CRC, 2016, 294 pages, ISBN-10: 1498746152. https://doi.org/10.1201/b19666
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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 )
- S. Abbas, M. Benchohra and G. M. N'Guérékata. Topics in Fractional Differential Equations. Springer Science & Business Media, 2012, 412 pages, ISBN-10: 1489995471.
- M. H. Annaby and Z. S. Mansour. Q-fractional Calculus and Equations. Springer, 2012, 340 pages, ISBN-10: 364230897X.
- 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.)
- 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.
- 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
- Y. Luo and Y. Chen. Fractional Order Motion Controls. John Wiley & Sons, 2012, 454 pages, ISBN-10: 1119944554. https://doi.org/10.1002/9781118387726
- 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
- I. Pan and S. Das. Intelligent Fractional Order Systems and Control: An Introduction. Springer, 2012, 316 pages, ISBN-10: 3642438520.
- 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
- S. Das and I. Pan. Fractional Order Signal Processing: Introductory Concepts and Applications. Springer Science & Business Media, 2011, 116 pages, ISBN-10: 3642231160.
- 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
- 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
- J. S. Leszczyński. An Introduction to Fractional Mechanics. Publishing Office of Czestochowa University of Technology, 2011, 128 pages, ISBN: 978-83-7193-494-0.
- 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
- 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
- I. Petráš. Fractional-order Nonlinear Systems: Modeling, Analysis and Simulation. Springer Science & Business Media, 2011, 218 pages, ISBN-10: 9783642181009.
- B. L. S. Prakasa Rao. Statistical Inference for Fractional Diffusion Processes. John Wiley & Sons, 2011, 280 pages, ISBN-10: 0470665688.
- 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.
- 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
- 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.
2010
- 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
- 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
- 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.
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- A. Khare. Fractional Statistics and Quantum Theory. World Scientific, 2005, 316 pages, ISBN-10: 9812561609. https://doi.org/10.1142/9789812567758
- G. M. Zaslavsky. Hamiltonian Chaos and Fractional Dynamics. Oxford University Press on Demand, 2005, 436 pages, ISBN-10: 0199535485.
2004
- 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
- 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
- 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
- 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
- R. Hilfer. Applications of Fractional Calculus in Physics. World Scientific, 2000, 472 pages, ISBN-10: 9810234570. https://doi.org/10.1142/9789812817747
1998
- 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
- 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
- N. K. Bliev. Generalized Analytic Functions in Fractional Spaces. Vol. 86. CRC Press, 1997, 160 pages, ISBN-10: 0582288614.
- 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
- I. V. Novozhilov. Fractional Analysis: Methods of Motion Decomposition. Springer Science & Business Media, 1997, 232 pages, ISBN-10: 1461286670.
1996
- B. Rubin. Fractional Integrals and Potentials. Chapman and Hall/CRC, 1996, 424 pages, ISBN-10: 0582253411.
- 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.
1995
- T. Chakraborty and P. Pietiläinen. The Quantum Hall Effects: Integral and Fractional. Vol. 85. Springer Science & Business Media, 1995, 302 pages, ISBN-10: 354058515X.
1993
- V. S. Kiryakova. Generalized Fractional Calculus and Applications. CRC press, 1993, 360 pages, ISBN-10: 0582219779.
- 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
- 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
- F. Wilczek. Fractional Statistics and Anyon Superconductivity. World scientific, 1990, 460 pages, ISBN-10: 9810200498. https://doi.org/10.1142/0961
1974
- 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