A mixed nonlinear time-fractional Rayleigh-Stokes equation

Abstract

This paper investigates a nonlinear time-fractional Rayleigh-Stokes equation with mixed nonlinearity containing a power-type function, a logarithmic function and an inverse time-forcing term. Applying Lagrange's mean value theorem and the compactness of the Sobolev embeddings, we estimate the complex Lipschitz property of mixed nonlinearity. We investigate the local well-posed results (local existence, regularity estimate, continuation) of the solutions in Hilbert scales space. Moreover, the global existence theory affiliated to the finite-time blow-up is considered.