Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations

Abstract

In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the application of the abstract results.

On the Study of Pseudo 𝒮-Asymptotically Periodic Mild Solutions for a Class of Neutral Fractional Delayed Evolution Equations

“…More information about this class of functions can be founded in [1,5,15], from which we find the following:…”

“…For example, in [4] the authors have examined the existence and uniqueness of pseudo S-asymptotically periodic solutions of the second-order abstract Cauchy problems. Another interesting class of the abstract fractional equations was analyzed in [5], where the authors have considered the following fractional integro-differential neutral equations…”

Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

“…Recently, Chang and Wei in [10] introduced the notion of pseudo S-asymptotically Bloch type periodic function on the real line and investigated the existence and uniqueness of pseudo S-asymptotically Bloch type periodic mild solutions to some semilinear evolution equations. It is noted that pseudo S-asymptotically Bloch type periodicity can be regarded as a generalization of S or pseudo S-asymptotic ω-periodicity which has been considerably studied, see for instance [13,20,22,23,24,26,27] and references cited therein. In particular, the concept of pseudo S-asymptotically ω-anti-periodic function on the real line as a special case was pointed out in [10].…”