Analytical solution of Abel integral equation arising in astrophysics via Laplace transform

The main aim of the present work is to propose a new and simple algorithm for Abel integral equation, namely homotopy perturbation transform method (HPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. Abel’s integral equation occurs in the mathematical modeling of several models in physics, astrophysics, solid mechanics and applied sciences. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.