Duality Between the Abaoub-Shkheam Transform and Some Important Integral Transforms

Abstract

Nowadays, integral transforms are the most appropriate techniques for finding the solution of typical problems because these techniques convert them into simpler problems. Finding the solution of initial value problems is the main use of integral transforms. Also, there are so many other applications of integral transforms in different areas of mathematics, statistics, and engineering, such as in solving improper integrals of the first kind, finding the solution of heat transfer problems, electrical networks, and signal processing problems. In this research paper, we will discuss connections between the Abaoub-Shkheam transform, a new integral transform type, and some effective integral transforms. Integral transforms of some typical functions are presented in a table to effectively illustrate the relationship between the Abaoub-Shkheam transform and some effectively mentioned integral transforms.