Homotopy analysis transform method for solving Abel’s integral equations of the first kind

In this paper, by combined homotopy analysis method and Laplace transform method, we produce a new powerful method and named homotopy analysis transform method. By using this method, we solve first kind singular integral equations of Abel type. Also, the convergence of the proposed method is proved. The numerical results show that the presented method is effective and accurate. Also, by plotting the h-curve, we show the convergence region of the examples.