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, an extension is paid to an idea of fractal and fractional derivatives which has
been applied to a number of ordinary differential equations to model a system of partial …

Many chemical systems exhibit a range of patterns, a noticeable and interesting class of
numerical patterns that arise in autocatalytic reactions which changes with increasing spatial …

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 …

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 …

This study focuses on the study of spatiotemporal and chaotic behavior in an extended non-
integer order dynamical systems which describe the spatial interaction between two …

In this paper, a robust numerical simulation technique based on the fractional Adams–
Bashforth and the Fourier spectral methods are formulated to explore some spatiotemporal …

An epidemic system of HIV/AIDS transmission is examined in this paper. The classical time
derivative is modelled with the Atangana-Baleanu nonlocal and nonsingular fractional …

In this paper, we model an ecological system consisting of a predator and two preys with the
newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu …