Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption

Shouguo Zhu (), Zhenbin Fan () and Gang Li ()
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Shouguo Zhu: Yangzhou University
Zhenbin Fan: Yangzhou University
Gang Li: Yangzhou University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 1, No 5, 47-64

Abstract: Abstract In this paper, an evolution system with a Riemann–Liouville fractional derivative is proposed and analyzed. With the help of a resolvent technique, a suitable concept of solutions to this system is formulated and the corresponding existence of solutions is demonstrated. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. Our work essentially generalizes previous results on optimal controls of all evolution systems. Finally, a simple example is presented to illustrate our theoretical results.

Keywords: Optimal controls; Resolvent; Riemann–Liouville derivative; 49J15; 47A10; 34K37 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-017-1119-y

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