A hybrid natural transform homotopy perturbation method for solving fractional partial differential equations

TL;DR

This paper introduces a hybrid analytical approach combining Natural Transform and Homotopy Perturbation methods to efficiently solve linear and nonlinear fractional partial differential equations with improved accuracy.

Contribution

It presents a novel hybrid method that reduces computational effort and avoids round-off errors in solving fractional PDEs, enhancing existing analytical techniques.

Findings

Successfully obtained exact solutions for fractional PDEs

Reduced computational complexity compared to traditional methods

Avoided round-off errors in calculations

Abstract

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical method is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear terms are calculated using He's polynomials. The proposed analytical method reduces the computational size, avoids round-off errors. Exact solutions of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.