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 paper, we shall review an approach by which we can seek higher order time
discretisation schemes for solving time fractional partial differential equations with …

We introduce a modified L1 scheme for solving time fractional partial differential equations
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …

This paper proposes a linearized fast high-order time-step** scheme to solve the time–
space fractional Schrödinger equations. The time approximation is done by using the fast L2 …

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 …

Alikhanov's high-order scheme for Caputo fractional derivatives of order α ∈ (0, 1) α∈(0, 1)
is generalised to nonuniform meshes and analysed for initial-value problems (IVPs) and …

The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

This paper is concerned with numerical solutions of time-fractional parabolic equations. Due
to the Caputo time derivative being involved, the solutions of equations are usually singular …

Stability and convergence of a time-weighted discrete scheme with nonuniform time steps
are established for linear reaction-subdiffusion equations. The Caupto derivative is …

Time-fractional initial-boundary value problems of the form are considered, where is a
Caputo fractional derivative of order and the spatial domain lies in for some. As we prove …