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The Elzaki Transform Homotopy Perturbation Method (ETHPM), a modified computational technique, is used in this article to solve the time-fractional reaction-diffusion equation that emerges in porous media. Herein fractional-order derivatives are considered in Caputo sense. To show how simple and effective the suggested method is, some specific and understandable examples are provided. The numerical results produced by the suggested technique show that the method is accurate and easy to use. The graphical illustrations of the approximate solutions to the porous media equation for different particular cases are the key characteristics of the current research. The solution obtained is very useful and significant to analyze the many physical phenomena. Keywords: Fractional calculus, Elzaki Transform Homotopy Perturbation Method (ETHPM), Fractional reaction-diffusion equations