Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators

Yong-Kui Chang (), Yatian Pei () and Rodrigo Ponce ()
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Yong-Kui Chang: Xidian University
Yatian Pei: Xidian University
Rodrigo Ponce: Universidad de Talca

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 6, 558-572

Abstract: Abstract This paper is mainly concerned with controlled stochastic evolution equations of Sobolev type for the Caputo and Riemann–Liouville fractional derivatives. Some sufficient conditions are established for the existence of mild solutions and optimal state-control pairs of the limited Lagrange optimal systems. The main results are investigated by compactness of fractional resolvent operator family, and the optimal control results are derived without uniqueness of solutions for controlled evolution equations.

Keywords: Fractional stochastic evolution equations of Sobolev type; Feasible pairs; Optimal controls; Resolvent operator; 34A08; 26A33; 93E20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-018-1314-5

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