Direct methods for singular integral equations and non-homogeneous parabolic PDEs

Abstract

In this article, the author presented some applications of the Laplace, $L^2$, and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. The obtained results reveal that the integral transform method is an effective tool and convenient