Haiyan Henry Zhang

This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grünwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).

This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. This expanded second edition bridges rigorous fractional calculus theory with cutting-edge engineering applications. It offers new case studies (e.g., stabilization control of a general class of fractional-order systems, fractional-order recurrent neural dynamical systems, etc.), enhanced MATLAB® implementations, and updated numerical methods for fractional-order controller design. Ideal for researchers and engineers, the book demystifies complex concepts like Grünwald-Letnikov and Caputo derivatives through real-world examples in robotics, chatter suppression, and engine control.