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 …

We develop spectral collocation methods for fractional differential equations with variable
order with two end-point singularities. Specifically, we derive three-term recurrence relations …

A fast finite volume method was developed for conservative space–time fractional diffusion
partial differential equations in two space dimensions. In the method a locally refined …

This paper develops a Galerkin approach for two-sided fractional differential equations with
variable coefficients. By the product rule, we transform the problem into an equivalent …

Abstract We proposed a Least Squares Finite Element Method (LSFEM) for the approximate
solution of Time fractional telegraph equation (TFTE). The method implemented the Vieta …

We present an analysis of existence, uniqueness, and smoothness of the solution to a class
of fractional ordinary differential equations posed on the whole real line that models a steady …

In this article we consider the approximation of a variable coefficient (two-sided) fractional
diffusion equation (FDE), having unknown u. By introducing an intermediate unknown, q, the …

In this work, we consider a boundary value problem involving Caputo derivatives defined in
the plane. We develop a fast locally refined finite volume method for variable-coefficient …

In this article a two-sided variable coefficient fractional diffusion equation (FDE) is
investigated, where the variable coefficient occurs outside of the fractional integral operator …

Fractional partial differential equations (FPDEs) provide very competitive tools to model
challenging phenomena involving anomalous diffusion or long-range memory and spatial …