Applied Mathematics & Optimization

, Volume 77, Issue 3, pp 443–462 | Cite as

The Solvability and Optimal Controls for Fractional Stochastic Differential Equations Driven by Poisson Jumps Via Resolvent Operators

Article

Abstract

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.

Keywords

Contraction mapping principle Fractional calculus Optimal controls Poisson jumps Solvability 

Mathematics Subject Classification

26A33 34A12 34A08 34K50 47H10 

Notes

Acknowledgments

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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsThe Gandhigram Rural Institute - Deemed UniversityGandhigramIndia

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