New trends in Laplace type integral transforms with applications

Abstract

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 Kd.V equation. Illustrative examples are also provided.

Keywords

• Keywords: Laplace transform
• Generalized Stieltjes transform
• Kelvin’s function
• Airy differential equation
• Korteweg – de Vries equation.