On Jan. 18, 2026, Dr. Chen was invited to give a seminar for BLS (U.S. Bureau of Labor Statistics) entitled "An Introduction to Fractional Order Thinking and Roughness-Informed Fractional Order Processing of Complex Signals".
Title: An Introduction to Fractional Order Thinking and Roughness-Informed Fractional Order Processing of Complex Signals
Abstract: Fractional calculus is about differentiation/integration of non-integer orders. Rejecting fractional calculus is like saying there is no other numbers between two neighboring integers. In this tutorial talk, I will explain the core motivation of fractional calculus by first showing the “core motivation” of (integer-order) calculus invented by Newton and Leibnitz which could be traced back to the time of Heraclitus of Ephesus. My concise messages are that the “integer order calculus” is driven by “the desire and the need” of “quantification of changes” while “non-integer order calculus” is by “the desire and the need of understanding complexities”. I then propose the FOT – fractional order thinking and the “better than the best” type of argument of applied fractional calculus. After explaining the triangular relationship between complexity-fractional calculus-IPL (inverse power law), I will share our recent thinking on “roughness” notions and roughness-informed signal processing of complex signals.
References:
- Judith V. Grabiner The Changing Concept of Change: The Derivative from Fermat to Weierstrass. Mathematics Magazine, Vol. 56, No. 4, September 1983 https://www.maa.org/sites/default/files/0025570x04690.di021131.02p02223.pdf
- H. Sun et al. “A new collection of real world applications of fractional calculus in science and engineering” https://doi.org/10.1016/j.cnsns.2018.04.019 Commun Nonlinear Sci Numer Simulat 64 (2018) 213–231.
- Bruce J West and YangQuan Chen. "Fractional Calculus for Skeptics I: The Fractal Paradigm". Vol. 1 of the CRC Press Book Series on Fractional Order Thinking in Exploring the Frontiers of STEM (Science Technology Engineering and Math) (FOT4STEM), May 2024, (146 pages) https://doi.org/10.1201/9781003468561
- Bruce J West and YangQuan Chen. "Fractional Calculus for Skeptics II: Quantifying Roughness". ibid, to appear, end of 2025
Biography (245 words):
(Photo) YangQuan Chen earned his Ph.D. from Nanyang Technological University, Singapore, in 1998. He had been a faculty of Electrical Engineering at Utah State University (USU) from 2000-12. He joined the School of Engineering, University of California, Merced (UCM) in summer 2012 teaching “Mechatronics”, “Engineering Service Learning”, “Unmanned Aerial Systems” and “Digital Twins” for undergraduates; “Fractional Order Mechanics”, “Linear Multivariable Control”, “Nonlinear Controls” and “Advanced Controls: Optimality and Robustness” for graduates. His research interests include mechatronics for sustainability, cognitive process control and smart control engineering enabled by digital twins, small multi-UAV based cooperative multi-spectral “personal remote sensing”, applied fractional calculus in controls, modeling and complex signal processing, distributed measurement and control of distributed parameter systems with mobile actuator and sensor networks. He was a Highly Cited Researcher by Clarivate Analytics from 2018 to 2021. He received Research of the Year awards from USU (12) and UCM (20). Most recently he started with Dr. Bruce J. West a new book series of CRC Press on FOT4STEM (Fractional Order Thinking in Exploring the Frontiers of STEM) and established a new section for Fractals and Fractional journal on “Optimization, big data and AI/ML”. His Google Scholar citations are over 60200 with H-index 105, H-10 index 689. His most recent books are “Fractional Calculus for Skeptics I: The Fractal Paradigm” (CRC 2024), “Fractional Calculus for Skeptics II: Quantifying Roughness” (CRC 2025). His lab website is http://mechatronics.ucmerced.edu/ and his publication list is at https://scholar.google.com/citations?user=RDEIRbcAAAAJ&hl=en (Email: ychen53@ucmerced.edu)
Created and last updated by Prof. YangQuan Chen 2/5/2026.
