A new fractional analytical approach for treatment of a system of physical models using Laplace transform

In this study, the Homotopy Perturbation Transform Method (HPTM) is performed to give approximate and analytical solutions of the rst order linear and nonlinear system of a time fractional partial dierential equation. The HPTM is a combined form of the Laplace transform, the homotopy perturbation method, and Heʹs polynomials. The nonlinear terms can be easily handled by the use of Heʹs polynomials. The proposed scheme nds the solutions without any discretization or restrictive assumptions, and is free of round-o errors, which, therefore, reduces the numerical computations to a great extent. The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described here in the Caputo sense. Numerical results show that the HPTM is easy to implement and accurate when applied to a time-fractional system of partial dierential equations.