Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations
Open Access
- 1 January 2014
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2014, 1-11
- https://doi.org/10.1155/2014/216919
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.Keywords
Funding Information
- National Natural Science Foundation of China (11271087, 61263006, 2013YB074, 12GXZ001, YCSZ2012062)
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