Discontinuity, Nonlinearity, and Complexity
The Solvability and Optimal Controls for Some Fractional Impulsive Equation with Finite Delay
Discontinuity, Nonlinearity, and Complexity 3(2) (2014) 133145  DOI:10.5890/DNC.2014.06.003
Xianghu Liu; Yanfang Li
School of Mathematics and Computer Science, Zunyi Normal College,563002, Zunyi,China
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Abstract
This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations withfinite delay. Firstly,we introduce the fractional calculus,Gronwall inequality, lerayschauder’sfixed point theorem,Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.
Acknowledgments
The authors thanks the referees for their careful reading of the manuscript and insightful comments, which help to improve the quality of the paper. We would also like to acknowledge the valuable comments and suggestions from the editors, which vastly contributed to improve the presentation of the paper.
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