A Study Of Fractional Differential And Integral Equations And Their Applications

Abstract

integral transforms namely the Laplace transform, Kamal newlinetransform, Sumudu transform, and physical interpretation of Riemann-Liouville left-hand and newlineright-hand sides fractional operators. Besides, this chapter sketches a brief history of special newlinefunctions of fractional calculus such as Mittag-Leffler functions (1903), Generalized Mittag- newlineLeffler function (1971), k-Mittaf-Leffler function, p-k Mittag-Leffler function, p,s,k Mittag- newlineLeffler function, S-function, R-function, G-function, which occur as the solutions of newlinefractional differential and integral equations. Further researchers introduced a brief history of newlinefractional calculus operators for integrals and derivatives and its applications in different newlineareas to solve many problems in applied science and engineering. Researcher defined some properties and important basic definitions on these special functions