Time-fractional nonlinear evolution equations with time-dependent constraints

Abstract: This article is devoted to presenting an abstract theory of time-fractional gradient flow equations for time-dependent convex functionals in real Hilbert spaces. The main results are concerned with the existence of strong solutions to time-fractional abstract evolution equations governed by time-dependent subdifferential operators. To prove these results, Gronwall-type lemmas for nonlinear Volterra integral inequalities and fractional chain-rule formulae are developed. Moreover, the obtained abstract results are applied to the initial-boundary value problem for time-fractional nonlinear parabolic equations on moving domains.