A New Fractional Integral Transform: Katugampola Aboodh Transform and Its Applications

Abstract

The Aboodh transform is a powerful tool in the analysis of signals and functions, particularly in the context of fractional calculus and signal processing. In this article, we introduce a new form of the Aboodh transform, which we refer to as the Katugampola Aboodh transform. This new definition is based on the Katugampola derivative, a generalization of the classical derivative that retains many of the essential properties of traditional calculus. We provide examples to reinforce the applicability of this new transform.

Keywords: Aboodh transform; fractional differential equation; Katugampola fractional derivative; Adomian polynomial.