We apply homotopy perturbation transformation method (combination of homotopy perturbation method and Laplace transformation) and homotopy perturbation Elzaki transformation method on nonlinear fractional partial differential equation (fpde) to obtain a series solution of the equation. In this case, the fractional derivative is described in Caputo sense. To avow the adequacy and authenticity of the technique, we have applied both the techniques to Fractional Fisher’s equation, time-fractional Fornberg-Whitham equation and time fractional Inviscid Burgers’ equation. Finally, we compare the results obtained from homotopy perturbation transformation technique with homotopy perturbation Elzaki transformation.
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers’ equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He’s polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
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