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

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

Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms

In this article, the author implemented the joint transform method, for solving the boundary value problems of time fractional heat equation. The results reveal that the integral transform method is reliable and efficient. Illustrative examples are also provided

Perturbation method for linear and non-linear fractional order systems and integral representation for evaluation of integrals

In the present work, the authors used the Laplace transform - perturbation method to solve certain linear and non-linear systems of fractional differential and difference equations with constant coefficients with the fractional derivatives in the Caputo sense. We also considered the problems of string vibrations in different cases with fractional damping. Another purpose of this article is to evaluate certain integrals. Illustrative examples are also provided