"This second volume of the multi-volume Fractional Calculus for Skeptics explores the con-cept 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 volumes foundational work advocating a fractal/fractional calculus par-adigm shift, this volume offers an in-depth exploration of the concept of "roughness," draw-ing parallels to what BenoƮt B. Mandelbrot originally intended to call the "Science of Rough-ness." The book introduces the novel concept of "body roughness" and demonstrates its prac-tical 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 Alzheimers disease, and the other involves biologically variable ven-tilation 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"-- Provided by publisher.
Fractional Calculus for Skeptics II : Quantifying Roughness