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.

Yi Yang is a postdoctoral researcher at The Chinese University of Hong Kong. He earned his Ph.D. from the School of Engineering Technology at Purdue University and received his M.S. from the University of Michigan–Ann Arbor. His research scope and interests lie in fractional-order nonlinear/adaptive/intelligent control in Mechatronics, Robotic Motion Planning, and Embodied Artificial Intelligence (AI).

Haiyan Henry Zhang is a Full Professor of Engineering Technology and the founding director of the Center for Technology Development at Purdue University. He received his Ph.D. from the University of Michigan–Ann Arbor in 1996. With a multidisciplinary engineering background and industry experience, his research focuses on analytical mechatronics and multidisciplinary mechanisms, advanced manufacturing control, and the design of hybrid electric vehicle powertrains.