Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …

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 …

This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

Stability and convergence of the L1 formula on nonuniform time grids are studied for solving
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …

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 …

This work suggested a new generalized fractional derivative which is producing different
kinds of singular and nonsingular fractional derivatives based on different types of kernels …

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 …

This article aims to fill in the gap of the second-order accurate schemes for the time-
fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are …

In this article, finite difference methods with non-uniform meshes for solving nonlinear
fractional differential equations are presented, where the non-equidistant stepsize is non …

A Newton linearized Galerkin finite element method is proposed to solve nonlinear time
fractional parabolic problems with non-smooth solutions in time direction. Iterative processes …