Decay solutions to retarded fractional evolution inclusions with superlinear perturbations

Abstract

In this paper, we consider a class of abstract fractional differential inclusion with finite delay in which the multi-valued nonlinearity is possibly superlinear. We analyze some sufficient conditions that ensure the global solvability of problem. Our main result is the existence of a compact set of decay solutions to our problem by estimating the measure of noncompactness and using the fixed point theory for a condensing map. The obtained results will be applied to a concrete polytope fractional differential system.

Long time behavior of solutions for time-fractional pseudo-parabolic equations involving time-varying delays and superlinear nonlinearities

“…Over the past few years, fractional functional differential equations (FrFDEs) in both finite and infinite dimensional spaces have been widely investigated in the literature by many researchers [1,2,13,16,24,28,29,30,35,36]. These studies are strongly motivated from the fact that FrFDEs are effective tools in the modeling various processes, phenomena arising from physics, biology, economics, engineering and other applied sciences, where the current state of such evolutionary processes depends on the past state [3,6,33].…”

“…This topic has been studied extensively by many authors and many notable contributions have been established in the last few years. We mention recent results concerning to the qualitative analysis on the behavior of solutions such as the Mittag-Leffler stability, asymptotic stability, weakly asymptotic stability and existence of decay solutions governed by FrFDEs [1,2,4,13,16,24,28,29,30].…”