Analysis of asymptotic behavior of the Caputo–Fabrizio time-fractional diffusion equation

Abstract

We use the continuous time random walk to analyze the asymptotic behavior of the Caputo–Fabrizio time-fractional diffusion equation (CF-tFDE). By evaluating the diffusion limit of the Laplace–Fourier transform of the solution to the CF-tFDE, we prove that the long-time limiting governing equation satisfies an integer-order Fickian diffusion equation. Numerical experiments are presented to verify the theoretical results.