This book refers to the fractional calculus development and the mathematical tools needed to solve fractional-order differential and integral equations. Very nice introduction and historical development of the problem of fractional calculus starting from Leibniz, Euler, Laplace, Fourier, Abel, Liouville, Riemann, Letnikov, Grünwald, Marchaud, etc are presented.
Various definitions of fractional derivatives and integrals and their properties are shown. The Laplace transform method for solving fractional differential and integral equation is presented. The Wayl fractional calculus is considered in a separate chapter of this book.
A historical overview of the fractional calculus is discussed, starting from the generalized tautochrone problem (1823) of Abel who for the first time applied the fractional calculus techniques in a physical problem, through the Heaviside operational calculus, the application of the fractional calculus by Liouville to problems in potential theory, etc.
Very interesting algebraic results, techniques of solving fractional differential equations by using complementary polynomials, reduction formulas and algebraic identities are presented in details. Such technique is applied by many authors for solving fractional order diffusion and wave equations, fractional Langevin equation describing anomalous diffusion processes, etc <span style="\"font-size:" 11pt;="" font-family:="" "stobiserif="" regular";\"=""> This is a book which should be read by any researcher in the field of fractional calculus and its application. Also I strongly recommend for all the readers interested in the field of mathematical physics.
