A unified presentation of certain families of non-Fuchsian differential equations via fractional calculus operators

Abstract

In recent years, many authors demonstrated the usefulness of 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. The main object of the present paper is to show how readily some recent contributions on this subject by several workers, involving various interesting classes of non-Fuchsian differential equations (including, for example, the Fukuhara and Tricomi equations and the celebrated Bessel and Whittaker equations), can be obtained (in a unified manner) by suitably applying some general theorems on (explicit) particular solutions of a certain family of linear ordinary fractional differintegral equations.