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 review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …

In this paper we construct a new difference analog of the Caputo fractional derivative (called
the L 2-1 σ formula). The basic properties of this difference operator are investigated and on …

In recent years, considerable attention has been devoted to distributed-order differential
equations mainly because they appear to be more effective for modelling complex …

In this article, a special point is found for the interpolation approximation of the linear
combination of multi-term fractional derivatives. The derived numerical differentiation …

As a natural generalization of the fractional Schrödinger equation, the variable-order
fractional Schrödinger equation has been exploited to study fractional quantum phenomena …

The present paper is devoted to constructing L2 type difference analog of the Caputo
fractional derivative. The fundamental features of this difference operator are studied and it …

In this paper, we develop an efficient finite difference/spectral method to solve a coupled
system of nonlinear multi-term time-space fractional diffusion equations. In general, the …

The distributed-order fractional diffusion equation is a generalization of the standard
fractional diffusion equation that can model processes lacking power-law scaling over the …

An efficient numerical technique is proposed to solve one-and two-dimensional space
fractional tempered fractional diffusion-wave equations. The space fractional is based on the …