On the PC $\mathcal{PC}$ -mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

Abstract

In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S-asymptotically ω-periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo-Sadovskii and Tichonov fixed-point theorems. Furthermore, an example to the fractional initial/boundary value Cauchy problem is concerned to illustrate our main results. MSC: 26A33; 26A42

Mixed monotone iterative technique for fractional evolution equations IS-asymptotically periodic problem with non-instantaneous impulses

“…In recent years, some achievements have been made in the study of fractional non-instantaneous impulsive differential equations, but the literature on this subject is still very limited. For the latest research on this topic, one can see the documents [38,43,44,22,32,40,3], and the references therein. It is worth noting that recently Saadati et al [32] studied the existence of P C-mild solutions for a class of abstract fractional evolution equations with non-instantaneous impulses.…”

“…For the latest research on this topic, one can see the documents [38,43,44,22,32,40,3], and the references therein. It is worth noting that recently Saadati et al [32] studied the existence of P C-mild solutions for a class of abstract fractional evolution equations with non-instantaneous impulses. As a part of their investigation, the existence of IS-asymptotically ω-periodic mild solutions based on the Hausdorff measure of noncompactness has been established.…”

Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

“…Motivated by above remark, Wang and Fečkan [24] have shown existence, uniqueness and stability of solutions of such general class of impulsive differential equations. To learn more about this kind of problems, we refer [25][26][27][28][29][30][31][32][33][34].…”

“…By virtue of the theory of measure of noncompactness associated with Darbo's and Darbo-Sadovskii's fixed point theorem. This technique was considered by Banas and Goebel [35] and subsequently used in many papers; see, for example, [33,[36][37][38][39].…”

S-asymptotically $ \omega $-periodic mild solutions and stability analysis of Hilfer fractional evolution equations

“…Later on Saadati et al [34], considered the following system of FDEs for obtaining SAP ω mild solutions.…”