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EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL DYNAMIC EQUATIONS WITH DELAY ON TIME SCALES
EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL DYNAMIC EQUATIONS WITH DELAY ON TIME SCALES
Journal of applied mathematics & informatics. 2015. May, 33(3_4): 275-292
  • Received : August 25, 2014
  • Published : May 30, 2015
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GAO ZHI-JUAN
FU XU-YANG
LI QIAO-LUAN

Abstract
This paper is mainly concerned with the existence of solution for nonlinear impulsive fractional dynamic equations on a special time scale.We introduce the new concept and propositions of fractional q-integral, q-derivative, and α-Lipschitz in the paper. By using a new fixed point theorem, we obtain some new existence results of solutions via some generalized singular Gronwall inequalities on time scales. Further, an interesting example is presented to illustrate the theory.
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