Certain Solutions of Abel’s Integral Equations on Distribution Spaces via Distributional Gα-Transform

Abstract

Abel’s integral equation is an efficient singular integral equation that plays an important role in diverse fields of science. This paper aims to investigate Abel’s integral equation and its solution using Gα-transform, which is a symmetric relation between Laplace and Sumudu transforms. Gα-transform, as defined via distribution space, is employed to establish a solution to Abel’s integral equation, interpreted in the sense of distributions. As an application to the given theory, certain examples are given to demonstrate the efficiency and suitability of using the Gα-transform method in solving integral equations.