Fractional Calculus

Abstract

Fractional calculus and applications are rapidly developing research directions in science and engineering at present.This book provides a systematic introduction to fractional calculus, focusing on the use of computer tools to directly solve problems in the field of fractional calculus and applications.The structure and general idea of this book are as follows: 7 Chap. 1 gives a review of the related fields; 7 Chap. 2 introduces some special functions commonly used in this field; 7 Chaps.3 and 4 introduce the evaluation of fractional-order derivatives and integrals of known functions or sampling points; 7 Chap.5 introduces the use of specially designed filters to find the fractional-order derivatives and integrals of signals when the signals are unknown in advance.Chapters 3 to 5 can also be understood as offline and online methods for evaluating fractional-order derivatives and integrals.7 Chapter 6 introduces the analytical and numerical solutions of linear fractional-order differential equations (FODEs), 7 Chap.7 introduces the "command-driven" solution of nonlinear FODEs, 7 Chap.8 introduces the block diagram-based solution of FODEs, and 7 Chap.9 introduces the solution of special FODEs (including implicit ones, delayed differential equations, differential equation boundary value problems, and partial differential equations) that were previously difficult or impossible to solve.Each part in the book is equipped with MATLAB general solution functions written by the author, whereas a new FOTF Toolbox is released with the book.The readers can directly use these reusable codes to reproduce the results in the book, and more importantly, use them to creatively solve practical problems and explore new knowledge.In 2015, I was invited by Prof. Li Changpin of the Department of Mathematics, Shanghai University, an internationally renowned scholar in the field of fractional calculus, to write a related monograph for his series "Fractional Calculus in Applied Science and Engineering".In 2017, my monograph Fractional-Order Control Systems: Fundamentals and Numerical Implementations was fortunately published as the first volume of the series in de Gruyter Publishing.The following year, the corresponding monograph in Chinese, Fractional-Order Calculus and Fractional-Order Control, was officially published by Science Press.This book was completed in collaboration with Dr. Bai Lu, School of Information Engineering of

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