ANALYTICAL STUDY FOR SOME FRACTIONAL PHYSICAL MODELS VIA NATURAL TRANSFORM PADE’ APPROXIMATION METHOD

This study proposes novel analytical approximate solutions of fractional physical models named the Natural transform Pade’ approximation method (NTPAM). It is a coupling of the natural transform method (NTM) and Pade’ approximation method (PAM). The NTM supplies a general, analytic, and exact solution. We obtain the analytic solution with a fast-gathering average and high fineness by applying PAM to the natural transform method chain solution. The main target of this study is to obtain new analytically exact and approximate solutions for fractional physical models via NTPAM. To evaluate the robustness of the present method, we compare our results with those of other known methods, such as the Laplace residual power series method, the Laplace transform method, the Sumudu transform method, and the exact solutions. The results show the quality, novelty, and generality of the proposed method.