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 …

We consider a class of numerical approximations to the Caputo fractional derivative. Our
assumptions permit the use of nonuniform time steps, such as is appropriate for accurately …

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 work, we present a second-order nonuniform time-stepping scheme for the time-
fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete …

This paper is concerned with numerical solutions of time-fractional nonlinear parabolic
problems by a class of $ L1 $-Galerkin finite element methods. The analysis of $ L1 …

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 …

Volterra partial integro-differential problems with weakly singular kernel attract a lot of
attentions in recent years, thanks to the numerous real world applications. Solving this kind …

In this article, a novel double reduction order technique and a newly constructed nonlinear
compact difference operator are developed on graded meshes to simulate the nonlocal …

The fractional derivatives include nonlocal information and thus their calculation requires
huge storage and computational cost for long time simulations. We present an efficient and …

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 …