Opuscula Math. 30, no. 4 (), 507-525
http://dx.doi.org/10.7494/OpMath.2010.30.4.507
Opuscula Mathematica

# 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.