An Approximate Analytical Solution of Coupled Nonlinear Fractional Diffusion Equations

In recent years, fractional reaction-diffusion models have been studied due to their usefulness and importance in many areas of mathematics, statistics, physics, and chemistry. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative. The resulting solutions spread faster than classical solutions and may exhibit asymmetry, depending on the fractional derivative used. In this paper, a fractional exponential operator is considered as a general approach for solving partial fractional differential equations. We develop an approach for solving coupled nonlinear fractional diffusion equations with nonlinear source terms. These solutions will be evaluated numerically based on approximation analytical solutions. Comparisons between the approximate analytical solution and numerical solutions are shown.