Fractional diffusion-advection equation with resetting: An analytical approach

Abstract

In this article, the fractional diffusion-advection equation with resetting is introduced to promote the theory of anomalous transport. The fractional equation describes a particle’s non-diffusive motion performing a random walk and is reset to its initial position. An analytical method is proposed to obtain the solution of the fractional equation with resetting via Fourier and Laplace transformations. We study the influence of the fractional-order and resetting rate on the probability distributions, and the mean square displacements are analyzed for different cases of anomalous regimes.