Abstract

We study the long time behavior of solutions for time-fractional pseudo-parabolic equation involving time-varying delays and nonlinear pertubations, where the nonlinear term allows to have a superlinear growth. Concerning the associated linear problem, we establish a variation of parameters formula of mild solution and prove some regularity estimates of resolvent operators. In addition, thanks to local estimates on Hilbert scales, fixed point arguments and a new Halanay type inequality, we obtain some results on the global solvability, stability, dissipativity and the existence of decay solutions to our problem.