内容介绍：In this talk, we will introduce fractional multi-phase models based on free energy gradient flows. We develop a fractional extension of a mass-conserving Allen–Cahn/Cahn-Hilliard phase field model that describes the mixture of two incompressible fluids. The fractional order controls the sharpness of the interface, which is typically diffusive in integer-order phase-field models. The spatial discretization is based on a spectral method. We will introduce several stabilized schemes for the temporal discretization including alternatively direction implicit (ADI) and a variant of scalar auxiliary variable (SAV) methods. Finally, we will present some numerical results to demonstrate the efficiency of the numerical methods in terms of stability and accuracy.