A novel numerical approach for solving generalized fractional Fisher's equation

Abstract This paper aims to construct a novel numerical technique, the General Transform Adomian Decomposition Method (GTADM), for obtaining approximate solutions of fractional generalized Fisher's equation (FGFE). The fractional order is in the sense of Caputo. By applying the General transform(GT) and its inverse, the fractional Fisher equation is simplified within the GT domain, facilitating the treatment of the equation without imposing restrictive assumptions on the variables, then we apply the Adomian Decomposition Method(ADM) to solve the newly obtained equation. Stability analysis is conducted to enhance the theoretical framework. The GTADM requires less computational work and exhibits faster convergence without discretization, linearization, or perturbation, thus preserving the integrity of the FGFE. A comparative analysis with ADM, homotopy perturbation Sumudu transforms method (HPSTM), and q-homotopy analysis transform method (q-HATM) is performed to demonstrate the efficiency and robustness of GTADM. The accuracy and reliability of the GTADM are validated through the computation of absolute and relative errors. Furthermore, 2D and 3D graphical representations, generated using Maple 21 and MATLAB to support this work. The numerical results and graphs clearly demonstrate the efficiency and robustness of the GTADM.