Motivated by the importance of study on the complex behaviors, which may be exhibited by
fractional order differential equations, this review paper focuses on dynamical fractional …

In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to
obtain energy stable schemes for a class of phase field models. This novel auxiliary variable …

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) …

The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a
finite difference scheme for the time-fractional Allen–Cahn (tFAC) equation. Some essential …

We propose a structure-preserving scheme and its error analysis for time-fractional Navier–
Stokes equations (TFNSEs) with periodic boundary conditions. The equations are first …

The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to
simulate various phase field models. To save the computational cost, a new SAV approach …

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 …

The positive definiteness of discrete time-fractional derivatives is fundamental to the
numerical stability (in the energy sense) for time-fractional phase-field models. A novel …

In this work, we establish the energy stability of high-order L2-type schemes for time-
fractional phase-field equations. We propose a reformulation of the discrete L2 operator …

The convergence of variable-step L1 scheme is studied for the time-fractional molecular
beam epitaxy (MBE) model with slope selection. A novel asymptotically compatible L 2 norm …