This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We derive the fractional Fokker-Planck equation for the densit...

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation ∂tu + (−∆) s u = 0, 0 < s < 1, posed in the whole space R with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative d...

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Fell...