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

Abstract

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 $\mathcal{S}$-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.

Keywords

• Fractional evolution equations
• Mild solutions
• S $\mathcal{S}$ -asymptotically ω-periodic solutions
• Tichonov fixed-point theorem
• Darbo–Sadovskii fixed-point theorem
• Measure of noncompactness