An Analytical Solution of Abel Integral Equation of the Second Kind in Coupling of Various Transform Methods via Homotopy Perturbation Transform Method

Abstract

In this paper analytical solution for Abel integral equation of the second kind in the coupling of the Laplace-Stieltjes, Kamal, Laplace-Carson and Aboodh transform method with homotopy perturbation transform method is introduced. Abel integral equation of the second occurs in several models in physical sciences, astrophysics, applied sciences etc. The numerical approach of the method is very simple and illustrates the accuracy, validity, and stability of the solution in form of the exact solution.