On the PC-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

• Published in: Boundary value problems Vol. 2019; no. 1; pp. 1 - 23
• Main Authors: Saadati, R., Pourhadi, E., Samet, B.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 06-02-2019; Hindawi Limited
• Subjects: Analysis; Approximations and Expansions; Boundary value problems; Cauchy problems; Darbo-Sadovskii fixed-point theorem; Difference and Functional Equations; Evolution; Fixed points (mathematics); Fractional evolution equations; Impulses; Matematik; Mathematical analysis; Mathematics; Mathematics and Statistics; Measure of noncompactness; Mild solutions; Ordinary Differential Equations; Partial Differential Equations; S-asymptotically -periodic solutions; Tichonov fixed-point theorem; 26A42; asymptotically; Measure of noncompactness; Fractional evolution equations; Darbo–Sadovskii fixed-point theorem; 26A33; periodic solutions; Mild solutions; Tichonov fixed-point theorem
• ISSN: 1687-2762; 1687-2770; 1687-2770
• DOI: 10.1186/s13661-019-1137-9

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.