Local fractional integral transforms and their applications (Q2790399)

I have great pleasure in contributing a review of this research monograph written by three eminent professors. Each one of them has done outstanding and basic research work and has got to his credit a number of research papers, books and monographs. The book contains five chapters. Chapter 1 gives an introduction to local fractional derivative and integral operators and provides their definitions and basic properties. Chapter 2 is on local fractional Fourier series. It deals with the basic idea, properties and theorems concerning local fractional Fourier series. Some of their applications to signal analysis and solutions of local fractional differential equations are also discussed. Chapter 3 and Chapter 4 deal with local fractional Fourier transform and local fractional Laplace transform, respectively. In these chapters, an introduction, definition and properties of the respective transform are presented and their applications to signal analysis and solving local fractional differential equations are discussed. Chapter 5 treats the variational iteration and decomposition methods and the coupling methods of the Laplace transform with them involved in the local fractional operators. These techniques are then used to solve the local fractional partial differential equations. The presentation of the subject matter is lucid, clear and is in the proper modern frame work.NEWLINENEWLINE The monograph contains six appendices, 26 figures, and six tables. The appendices E and F as well as tables E.1 and F.1 for local fractional Fourier and Laplace transform operators provide very useful material for research workers interested in applying these ideas in various fields of science and engineering. The book has a bibliography comprising 129 useful entries.NEWLINENEWLINE The book is indeed a boon to all those who are interested in the field of local fractional integral transforms and want to further develop this live and useful branch of mathematics.