内容紹介

This book is the third edition of my book published under the same title. In this third edition, theorems about the chain rule for differentiation of a composite function, fractional differ-integration of a composite function, and the Laplace transform of fractional differ-integration of a function are added to the previous editions. In this book, a theory of fractional calculus is formulated by an operator-based method. A general operator called the p-operator which satisfies Leibniz's rule is used instead of a differentiation operator in classical calculus. A function sequence generated by repeated applications of the p-operator to a function belonging to some specified function space plays an important role in constructing this theory. It is shown that this theory can be extended to a theory on a coset space consisting of the equivalence sets of generalized functions. Under this theory, various special functions of non-negative integer degree can be extended to complex degrees. Several typical problems in mathematics and physics are treated by this theory to illustrate its applications. This book will benefit advanced students and researchers who are interested in fractional calculus.