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EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL DYNAMIC EQUATIONS WITH DELAY ON TIME SCALES
GAO, ZHI-JUAN,FU, XU-YANG,LI, QIAO-LUAN The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.3
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.
Existence of solution for impulsive fractional dynamic equations with delay on time scales
Zhi-Juan Gao,Xu-Yang Fu,Qiao-Luan Li 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.3
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 $\alpha$-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.