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 …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …

In this paper, we develop a new meshless method for solving a wide class of time-fractional
partial differential equations with general space operators in 2D and 3D regular and …

We develop proper correction formulas at the starting k-1 steps to restore the desired k th-
order convergence rate of the k-step BDF convolution quadrature for discretizing evolution …

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional
subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where …

This paper focusses on the numerical solution of the nonlinear time-fractional telegraph
equation formulated in the Caputo sense. This model is a useful description of the neutron …

In this article, a finite difference/finite element algorithm, which is based on a finite difference
approximation in time direction and finite element method in spatial direction, is presented …

Starting with the asymptotic expansion of the error equation of the shifted Grünwald–
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …

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 …