Over the past several decades, there has been a proliferation of epidemiological models
with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These …

This paper considers the dynamical properties of a space and time discrete fractional
reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The …

Our study focuses on fractional order compartment models derived from underlying physical
stochastic processes, providing a more physically grounded approach compared to models …

This study aims to validate the hypothesis that the pharmacokinetics of certain drug regimes
are better captured using fractional order differential equations rather than ordinary …

We consider new numerical schemes to solve two different systems of nonlinear fractional
reaction subdiffusion equations. These systems of equations model the reversible reaction …

Continuous time random walks, which generalize random walks by adding a stochastic time
between jumps, provide a useful description of stochastic transport at mesoscopic scales …

We have introduced a new explicit numerical method, based on a discrete stochastic
process, for solving a class of fractional partial differential equations that model reaction …

A generalised advection equation with a time fractional derivative is derived from a
continuous time random walk on a one-dimensional lattice, with power law distributed …

We derive the generalized master equations for a stochastic process representing
populations entering, leaving, or waiting in compartments at discrete times. This discrete …

The flow structure in natural rivers may change due to the disturbance of vegetation, further
affecting the transport of pollutants and sediment (Liu et al.). In this paper, the random …