Opuscula Math. 30, no. 4 (2010), 507-525
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.
Mathematics Subject Classification: 45N05, 93C25.
- Received: 2010-03-25.
- Revised: 2010-04-12.
- Accepted: 2010-04-17.