On some impulsive fractional differential equations in Banach spaces

Abstract

This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of \(PC\)-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

Keywords

• fractional differential equations with impulses
• nonlinear impulsive singular version of the Gronwall inequality
• \(PC\)-mild solutions
• existence