Solution of Some Non-Homogeneous Fractional Integral Equations by Aboodh Transform

Abstract

The present paper introduces the Aboodh transform technique as a method for obtaining solutions to a class of non-homogeneous fractional integral equations. The emphasis is placed on equations characterized by expressions involving Riemann-Liouville fractional integrals of orders $1,$ $\frac{1}{2},$ and $\frac{1}{3}.$ The paper includes illustrative examples that demonstrate the application of the Aboodh transform technique. These examples elucidate how the technique can effectively yield solutions for specific instances of the mentioned equations. The obtained solutions are presented in the form of Mellin-Ross functions.