Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations

Abstract

<p style='text-indent:20px;'>We study the generalized Rayleigh-Stokes problem involving a fractional derivative and nonlinear perturbation. Our aim is to analyze some sufficient conditions ensuring the global solvability, regularity and asymptotic stability of solutions. In particular, if the nonlinearity is Lipschitzian then the mild solution of the mentioned problem becomes a classical one and its convergence to equilibrium point is proved.</p>