The pattern formation process is closely associated with a class of reaction-diffusion
problems arising in mathematical biology and chemistry which has generated a lot of …

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the
two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed …

Impulse propagation in biological tissues is known to be modulated by structural
heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity …

In this work, the solution of Riesz space fractional partial differential equations of parabolic
type is considered. Since fractional-in-space operators have been applied to model …

The inherent heterogeneities of many geophysical systems often gives rise to fast and slow
pathways to water and chemical movement. One approach to model solute transport through …

We derive a fractional Cahn--Hilliard equation (FCHE) by considering a gradient flow in the
negative order Sobolev space H^-α, α∈0,1, where the choice α=1 corresponds to the …

In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

Recently a new fractional differentiation was introduced to get rid of the singularity in the
Riemann-Liouville and Caputo fractional derivative. The new fractional derivative has then …

In this article, a class of two-dimensional Riesz space fractional diffusion equations is
considered. Some fractional spaces are established and some equivalences between …

We consider numerical methods for solving the fractional-in-space Allen–Cahn equation
which contains small perturbation parameters and strong nonlinearity. A standard fully …