The Solvability and Optimal Controls for Fractional Stochastic Differential Equations Driven by Poisson Jumps Via Resolvent Operators
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In this manuscript, we investigate the solvability and optimal controls for fractional stochastic differential equations driven by Poisson jumps in Hilbert space by using analytic resolvent operators. Sufficient conditions are derived to prove that the system has a unique mild solution by using the classical Banach contraction mapping principle. Then, the existence of optimal control for the corresponding Lagrange optimal control problem is investigated. Finally, the derived theoretical result is validated by an illustrative example.
KeywordsContraction mapping principle Fractional calculus Optimal controls Poisson jumps Solvability
Mathematics Subject Classification26A33 34A12 34A08 34K50 47H10
This work is supported by Council of Scientific and Industrial Research, Extramural Research Division, Pusa, New Delhi, India under the Grant No. 25(0217)/13/EMR-II. The authors would like to express their deep gratitude to the Editor-in-Chief, associate editor and the anonymous referees for their careful reading and valuable suggestions to improve the quality of this manuscript.
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