The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2

Xianghu Liu; Zhenhai Liu; Maojun Bin

doi:10.1155/2014/142067

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Home > Journals > Abstr. Appl. Anal. > Volume 2014 > Article

2014 The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order

1< \alpha <2

Xianghu Liu, Zhenhai Liu, Maojun Bin

Abstr. Appl. Anal. 2014: 1-9 (2014). DOI: 10.1155/2014/142067

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Abstract

We study the existence of solutions and optimal controls for some fractional impulsive equations of order $1< \alpha <2$ . By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.

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Xianghu Liu. Zhenhai Liu. Maojun Bin. "The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order $1< \alpha <2$ ." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/142067