This paper investigates a two-dimensional Riemann–Liouville distributed-order space fractional diffusion equation (RLDO-SFDE). However, many challenges exist in deriving analytical solutions for dynamic systems. Efficient and reliable methods need to be explored solving the RLDO-SFDE numerically. We develop an alternating direction implicit scheme prove that numerical method is unconditionally ...

A reaction–diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their stability are analyzed analytically, and relationships between stability of the rest points of the non-distributed replicator equation and distributed system are sho...

In order to model fundamental cell biological processes including the transcription, translation, and nuclear membrane transport of biological molecules within a eukaryotic cell it is necessary to be able to approximate the stochastic reaction and diffusion of a small number of molecules in the complex three dimensional geometry of a cell. For this reason a method is developed that incorporates...

Abstract The main propose of this paper is presenting an efficient numerical scheme to solve WSGD for one- and two-dimensional distributed order fractional reaction–diffusion equation. proposed method based on B-spline basics in collocation which involve Caputo-type derivatives $$0 < \alpha 1$$ 0 &l..;.

In this article, the iterative transformation method and homotopy perturbation are applied to calculate solution of time-fractional Cauchy-reaction diffusion equations. technique, Shehu is combined iteration techniques. Four examples examined show validation efficacy present methods. The approximate solutions achieved by suggested methods indicate that approach easy apply given problems. Moreov...

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative o...