Fractional Calculus for Skeptics II

This second volume of the multi-volume Fractional Calculus for Skeptics explores the concept of "e;roughness"e; 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 "e;roughness,"e; drawing parallels to what Benoit B. Mandelbrot originally intended to call the "e;Science of Roughness."e; The book introduces the novel concept of "e;body roughness"e; and demonstrates its practical applications through two case studies of "e;roughness-informed rehabilitation therapy"e; 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 "e;take-home messages."e;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.