Asymptotic Estimates for Fractional Diffusion Equation with Caputo-Fabrizio Derivative

In this paper, we estimate the solution of the time-fractional reaction-diffusion equation with Caputo-Fabrizio derivative. The governing fractional reaction-diffusion equation is solved using Mellin inversion. As an example problem, we analyze the fractional reaction-diffusion equation with varying fractional operator values. After solving the governing equation, we obtain the first term approximation of the solution. Based on these results, we numerically evaluate the asymptotic behavior of both the solution and the first-term approximation. Additionally, we discuss the residue of the solution and its first term approximation.