Euler-Type Non-Homogeneous Differential Equations with Three Liouville Fractional Derivatives

Abstract

This paper deals with the study of linear non-homogeneous ordinary differential equations with three right-hand sided Liouville derivatives of fractional order. Using the direct and inverse Mellin transforms and the residue theory, explicit solutions of the considered equations are established in terms of the generalizedWright functions, of the generalized hypergeometric functions and of the Euler psi-function. The corresponding results are deduced for ordinary differential equations of Euler type. Examples are given.

2000 Mathematics Subject Classification: 34A05, 26A33, 44A99, 33C20, 33C99

Key Words and Phrases: linear differential equations with Liouville fractional derivatives, ordinary differential equations, explicit solutions, Mellin transforms, generalizedWright function, generalized hypergeometric function, Euler psi-function