Abstract and Applied Analysis

Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations

Xue Pan, Xiuwen Li, and Jing Zhao

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Abstract

We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. Then, by using generally mild conditions of cost functional, we extend the existence result of optimal controls to the Riemann-Liouville fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 216919, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276913

Digital Object Identifier
doi:10.1155/2014/216919

Mathematical Reviews number (MathSciNet)
MR3198165

Zentralblatt MATH identifier
07021949

Citation

Pan, Xue; Li, Xiuwen; Zhao, Jing. Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 216919, 11 pages. doi:10.1155/2014/216919. https://projecteuclid.org/euclid.aaa/1412276913


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