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) isperformed to give approximate and analytical solutions of the rst order linear andnonlinear system of a time fractional partial dierential equation. the hptm is a combinedform of the laplace transform, the homotopy perturbation method, and he's polynomials.the nonlinear terms can be easily handled by the use of he's polynomials. the proposedscheme nds the solutions without any discretization or restrictive assumptions, and is freeof 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 easilycomputable components. the fractional derivatives are described here in the caputo sense.numerical results show that the hptm is easy to implement and accurate when appliedto a time-fractional system of partial dierential equations.