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 …

New variable-order fractional chaotic systems are proposed in this paper. A concept of short
memory is introduced where the initial point in the Caputo derivative is varied. The fractional …

This paper investigates chaotic behavior and stability of fractional differential equations
within a new generalized Caputo derivative. A semi–analytical method is proposed based …

In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …

We consider the initial/boundary value problem for a diffusion equation involving multiple
time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space …

We develop an exponentially accurate fractional spectral collocation method for solving
steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of …

In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-
order multi-term subdiffusion equation. The L1 method on graded meshes is employed in …

In this paper, an efficient and accurate spectral numerical method is presented for solving
second-, fourth-order fractional diffusion-wave equations and fractional wave equations with …

In this article, we first propose a new numerical technique based upon a certain two-
dimensional extended differential transform via local fractional derivatives and derive its …

The multi-term time-fractional diffusion equation is a useful tool in the modeling of complex
systems. This paper aims to develop a high order numerical method for solving multi-term …