New trends in Laplace type integral transforms with applications

Abstract

In this paper, the authors provided a discussion on one and two dimensional Laplace transforms and generalized Stieltjes transform and their applications in evaluating special series and integrals. Finally, we implemented the joint Laplace -Fourier transforms to construct exact solution for a variant of the KdV equation. Illustrative examples are also provided.

Non-homogenous KdV and coupled sub-ballistic fractional PDEs

“…Several methods have been introduced to solve fractional differential equations, the popular Laplace transform method, [1], [2], [3], [12], the Fourier transform method [11], the iteration method [18] and operational method [11], [6]. However, most of these methods are suitable for special types of fractional differential equations, mainly the linear with constant coefficients.…”