Certain operators of fractional calculus and their applications to differential equations

Abstract

In many recent works, one can find remarkable demonstrations of the usefulness of certain fractional calculus operators in the derivation of (explicit) particular solutions of a number of linear ordinary and partial differential equations of the second and higher orders. Our main objective in the present sequel to these earlier works, is to show how readily and systematically some recent contributions on this subject, involving linear ordinary and partial differential equations of order m (m ϵ N) , can be obtained (in a unified manner) by suitably appealing to some general theorems on (explicit) particular solutions of a certain family of linear ordinary fractional differintegral equations.