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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


The Solvability and Optimal Controls for Some Fractional Impulsive Equation with Finite Delay

Discontinuity, Nonlinearity, and Complexity 3(2) (2014) 133--145 | 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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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, leray-schauder’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.


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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