Comparison of homotopy perturbation transform method and fractional Adams–Bashforth method for the Caputo–Prabhakar nonlinear fractional differential equations

We study two numerical techniques based on the homotopy perturba tion transform method (HPTM) and the fractional Adams–Bashforth method (FABM) for solving a class of nonlinear time-fractional differential equations involving the Caputo–Prabhakar fractional derivatives. In this manuscript, the convergence for numerical solutions obtained using HPTM and the con vergence and stability for numerical solutions obtained using FABM are inves tigated. We compare the solutions obtained by the HPTM and the FABM for some nonlinear time-fractional differential equations. Moreover, some numer ical examples are demonstrated in order to show the validity and reliability of the suggested methods.

Keywords:

onlinear time-fractional differential equations , Fractional Homotopy perturbation transform method , Fractional Adams–Bashforth method , Caputo–Prabhakar fractional derivative