The Novel Numerical Solutions for Time-Fractional Fishers Equation

Abstract

A new method for solving time-fractional partial differential equations (TFPDEs) is proposed in the paper. It is known as the fractional Kamal transform decomposition method (FKTDM). TFPDEs are approximated using the FKTDM. The FKTDM is particularly effective for solving various types of fractional partial differential equations (FPDEs), including time-fractional equations with Caputo or Caputo-Fabrizio derivatives, space-fractional equations involving Riesz-type operators, and coupled time-space fractional systems. It is well-suited for linear and weakly nonlinear problems, especially when combined with iterative techniques like the homotopy analysis method (HAM). Furthermore, FKTDM efficiently handles models with nonsingular kernels, making it a powerful tool for accurately modeling memory effects and anomalous diffusion in complex physical systems. The Caputo sense is used to define fractional derivatives. Also, MAPLE software displays the 2D and 3D graphs of the solutions to a few nonlinear TFPDEs. Besides, the FKTDM was evaluated against the q-homotopy analysis transform method, yielding superior results.MSC2020 Classification35C05, 35C07, 35C08, 35Q53, 76B25