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Optimal controls for Riemann-Liouville fractional evolution systems without Lipschitz assumption. (English) Zbl 1378.49004

Summary: 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.

MSC:

49J15 Existence theories for optimal control problems involving ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
47A10 Spectrum, resolvent
34K37 Functional-differential equations with fractional derivatives
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