Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

In this paper, we investigate the finite volume method (FVM) for a distributed-order space-
fractional advection–diffusion (AD) equation. The mid-point quadrature rule is used to …

This paper proposes the alternating direction implicit (ADI) numerical approaches for
computing the solution of multi-dimensional distributed-order fractional integrodifferential …

In this paper, we shall present the alternating direction implicit (ADI) Galerkin finite element
method (FEM) for solving the distributed-order time-fractional mobile–immobile equation in …

Numerical simulation technique of two-dimensional variable-order time fractional advection-
diffusion equation is developed in this paper using radial basis function-based differential …

In this paper, we construct and analyze a Legendre spectral-collocation method for the
numerical solution of distributed-order fractional initial value problems. We first introduce …

The fractional advection–diffusion problem coupled with incompressible Navier–Stokes
equations is important in science and engineering. In this paper, a fresh lattice Boltzmann …

This study proposes a scale-dependent finite difference method (S-FDM) to approximate the
time fractional differential equations (FDEs), using Hausdroff metric to conveniently link the …

In this paper, a new numerical approximation is discussed for the two-dimensional
distributed-order time fractional reaction–diffusion equation. Combining with the idea of …

Fractional differential equations have been proved to be powerful tools for modelling
anomalous diffusion in many fields of science and engineering. However, when comes to …