Fractional Calculus and Its Applications

This chapter reviews the basics of fractional calculus and discusses some of its applications. It describes gamma function, which was introduced by Euler, is a generalization of the factorial to noninteger values. The chapter explains Mittag-Leffler function, which is an extension of the exponential function to arbitrary real numbers. It also explains Laplace transform, which is commonly used in the solution of differential equations. The chapter deals with fractional integro-differentials. There are several definitions of the fractional integro-differentials. Each of the definitions has its advantages and drawbacks and the choice depends mainly on the purpose and the area of application. The three most frequently used definitions for the general fractional integro-differentials are: the Riemann-Liouville, the Gr252nwald-Letnikov definition, and the Caputo definition. Most of the applications of fractional differential equations (FDEs) involve relaxation and oscillation models. The chapter begins by reviewing the regular differential equations of these two models.

Перевод пока недоступен