Explicit solutions of some linear ordinary and partial fractional differintegral equations

Abstract

In recent years, many authors demonstrated the usefulness of some fractional calculus operators in the derivation of (explicit) particular solutions of a significantly large number of linear ordinary and partial differential equations of the second and higher orders. The main object of the present paper is to show how readily several recent contributions on this subject, involving second- as well as third-order linear ordinary and partial differential equations, can be obtained (in a unified manner) by appropriately applying some general theorems on (explicit) particular solutions of a certain family of linear ordinary and partial fractional differintegral equations.