This paper comprises of a finite difference method with implicit scheme for the Riesz fractional reaction–diffusion equation (RFRDE) by utilizing the fractional-centered difference for approximating the Riesz derivative, and consequently, we obtain an implicit scheme which is proved to be convergent and unconditionally stable. Also a novel analytical approximate method has been dealt with namely optimal homotopy asymptotic method (OHAM) to investigate the solution of RFRDE. The numerical solutions of RFRDE obtained by proposed implicit finite difference method have been compared with the solutions of OHAM and also with the exact solutions. The comparative study of the results establishes the accuracy and efficiency of the techniques in solving RFRDE. The proposed OHAM renders a simple and robust way for the controllability and adjustment of the convergence region and is applicable to solve RFRDE.

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