Solution of Some Non-Homogeneous Fractional Integral Equations by Aboodh Transform (Journal of Nonlinear Modeling and Analysis, 2024)
The present paper introduces the Aboodh transform technique asa method for obtaining solutions to a class of non-homogeneous fractionalintegral 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 ofthe Aboodh transform technique. These examples elucidate how the techniquecan effectively yield solutions for specific instances of the mentioned equations.The obtained solutions are presented in the form of Mellin-Ross functions.
Keywords: Fractional differential equations; Aboodh transform; fractional integral equations; Mellin-Ross function; Riemann-Liouville fractional integral.