Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses

Abstract

Abstract In this paper, we study periodic boundary value problems of fractional semilinear integro-differential equations with non-instantaneous impulses in Banach spaces. By the measure of noncompactness, the theory of β-resolvent family, and the fixed point theorem, we obtain several sufficient conditions on the existence of mild solutions for such problems. Finally, an example is given to show the main results of this paper.

Keywords

• Fractional semilinear integro-differential equation
• Measure of noncompactness
• Non-instantaneous impulses
• β-resolvent operator family