Fractional Calculus for Skeptics I : The Fractal Paradigm

This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research.

Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem.

The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.

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 PhD 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.