This second volume of the multi-volume Fractional Calculus for Skeptics explores the concept of “roughness” and its applications in complex systems. It demonstrates how fractional calculus offers valuable insights into modeling real-world phenomena that traditional calculus struggles to address.

Building on the first volume’s foundational work advocating a fractal/fractional calculus paradigm shift, this volume offers an in-depth exploration of the concept of “roughness,” drawing parallels to what Benoît B. Mandelbrot originally intended to call the “Science of Roughness.” The book introduces the novel concept of “body roughness” and demonstrates its practical applications through two case studies of “roughness-informed rehabilitation therapy” with closed-loop control systems. One study involves non-invasive, 40-Hz gamma-frequency sensory stimulation for Alzheimer’s disease, and the other involves biologically variable ventilation using roughness-informed, closed-loop control. The four chapters are complemented by valuable appendices and essential chapter-end references, as well as insightful “take-home messages.”

This book will appeal to students, researchers, and professionals in STEM fields, including engineering, physics, biology, biomedicine, control engineering, rehabilitation, big data, and machine learning.

Author Biography

Bruce J. West, a Physics PhD from the University of Rochester 1970, was the Chief Scientist in Mathematical and Information Science at the Army Research Office of the US, 1999–2021. His awards include the Presidential Meritorious Rank Award 2012 (Obama) and the Presidential Distinguished Rank Award 2017 (Trump).

YangQuan Chen, a Clarivate Highly Cited Researcher, earned his Ph.D. from Nanyang Technological University, Singapore, in 1998. He is a professor at the School of Engineering, University of California, Merced. His research interests include smart control engineering via digital twins and applied fractional calculus in STEM.

We are committed to protecting your rights under the Consumer Guarantees Act and working with our suppliers to assist with warranty claims. Products sold by Mighty Ape will be covered by a Manufacturer's Warranty for at least a one-year period from the date of purchase.

Your warranty will cover any manufacturing defects which, if existing, will present themselves within this warranty period.

Your warranty will not cover normal wear and tear, faults caused by misuse, and accidents which cause damage or theft caused after delivery. Using the product in a way it is not designed for will void your warranty.

Please refer to our Help Centre for more information.