• ANALYTICAL SOLUTION OF ABEL’S INTEGRAL EQUATION OF THE FIRST KIND BY USING q-HOMOTOPY ANALYSIS TRANSFORM METHOD

Abstract

In this paper, the analytical solution of Abel's integral equation of the first kind is investigated by using the q-homotopy analysis transform method (q-HATM). The q-HATM is a hybrid method that combines the q-homotopy analysis method (q-HAM) and the Laplace transform method (LTM). The analytical results obtained by the proposed method are in series form, indicating that the approach is simple to implement and computationally appealing.