Opuscula Math. 30, no. 4 (2010), 507-525
http://dx.doi.org/10.7494/OpMath.2010.30.4.507

 
Opuscula Mathematica

On some impulsive fractional differential equations in Banach spaces

JinRong Wang
W. Wei
YanLong Yang

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.

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  • JinRong Wang
  • Guizhou University, College of Science, Guiyang, Guizhou 550025, P.R. China
  • W. Wei
  • Guizhou University, College of Science, Guiyang, Guizhou 550025, P.R. China
  • YanLong Yang
  • Guizhou University, College of Technology, Guiyang, Guizhou 55004, P.R. China
  • Received: 2010-03-25.
  • Revised: 2010-04-12.
  • Accepted: 2010-04-17.
Opuscula Mathematica - cover

Cite this article as:
JinRong Wang, W. Wei, YanLong Yang, On some impulsive fractional differential equations in Banach spaces, Opuscula Math. 30, no. 4 (2010), 507-525, http://dx.doi.org/10.7494/OpMath.2010.30.4.507

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