Time-fractional Cahn–Hilliard equation: Well-posedness, degeneracy, and numerical solutions

In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law diffusion. This model describes process phase separation nonlocal memory effects. We analyze existence, uniqueness, and regularity weak solutions equation. regard, consider degenerating mobility functions free energies Landau, Flory--Huggins double-obstacle type. apply Faedo-Galerkin method to system, energy estimates, use compactness theorems pass limit in discrete form. order compensate for missing chain rule fractional derivatives, prove inequality semiconvex functions. The work concludes numerical simulations sensitivity analysis showing influence power. Here, convolution quadrature scheme component, mixed finite element space discretization.