**Authors: **Ahmed Entesar^{1} & Omar Saber^{2} & Waleed Al-Hayani^{3}

^{1&2&3}Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Iraq

**Abstract: **In this work, the Homotopy Analysis Method (HAM) is applied to solve fractional Partial Differential Equations (PDEs). The solution of HAM has improved the results by using Genetic Algorithm (GA). The hybrid method (proposed) is applied for types of problems where analytical solutions approximate are obtained. Numerical experiments are also presented.

**Keywords: **Homotopy Analysis Method (HAM), Genetic Algorithm (GA), Heat Like Equations, Wave Like Equations, Fractional Calculus

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