An efficient technique for solving the space-time fractional reaction-diffusion equation in porous media. (English) Zbl 07848617
Summary: In this paper, we obtained the approximate numerical solution of space-time fractional-order reaction-diffusion equation using an efficient technique homotopy perturbation technique using Laplace transform method with fractional-order derivatives in Caputo sense. The solution obtained is very useful and significant to analyze the many physical phenomenons. The present technique demonstrates the coupling of the homotopy perturbation technique and Laplace transform using He’s polynomials for finding the numerical solution of various non-linear fractional complex models. The salient features of the present work are the graphical presentations of the approximate solution of the considered porous media equation for different particular cases and reflecting the presence of reaction terms presented in the equation on the physical behavior of the solute profile for various particular cases.
MSC:
| 35Rxx | Miscellaneous topics in partial differential equations |
| 26Axx | Functions of one variable |
| 34Axx | General theory for ordinary differential equations |
Keywords:
reaction-diffusion equation; fractional derivatives; He’s polynomials; porous media equationReferences:
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