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 …

In this work, we propose a Crank--Nicolson-type scheme with variable steps for the time
fractional Allen--Cahn equation. The proposed scheme is shown to be unconditionally …

In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …

In this study, we investigate the intial value problem (IVP) for a time-fractional fourth-order
equation with nonlinear source terms. More specifically, we consider the time-fractional …

Adaptive second-order Crank--Nicolson time-stepping methods using the recent scalar
auxiliary variable (SAV) approach are developed for the time-fractional molecular beam …

A time-fractional Allen-Cahn initial-boundary value problem is considered, where the
bounded spatial domain Ω lies in R d for some d∈{1, 2, 3} and has smooth boundary or is …

We construct and analyze the variable-step scheme to efficiently solve the space-time
fractional Cahn–Hilliard equation in two dimensions. The associated variational energy …

We present a collocation approach based on redefined cubic B-spline (RCBS) functions and
finite difference formulation to study the approximate solution of time fractional Allen–Cahn …

There exists a well defined energy for classical phase-field equations under which the
dissipation law is satisfied, ie, the energy is non-increasing with respect to time. However, it …

We consider a time-fractional Cahn–Hilliard equation where the conventional first-order time
derivative is replaced by a Caputo fractional derivative of order. Based on an a priori bound …