Exponential Behavior and Optimal Control Analysis for a Class of Fractional Stochastic Hemivariational Inequalities of Order r∈(1,2) With Poisson Jumps

• Published in: Mathematical methods in the applied sciences Vol. 48; no. 8; pp. 8961 - 8974
• Main Authors: Dineshkumar, Chendrayan, Hoon Jeong, Jae, Hoon Joo, Young
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.05.2025
• Subjects: Clarke's subdifferential; Control systems; Fixed points (mathematics); Fractional calculus; fractional derivative; hemivariational inequalities; Inequalities; mild solution; multivalued functions; Operators; Optimal control; sectorial operators; stochastic equation; Stochastic systems
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.10767

ABSTRACT In this paper, we deal with the exponential behavior for fractional stochastic neutral hemivariational inequalities of order r∈(1,2)$$ r\in \left(1,2\right) $$ with sectorial operators and Poisson jumps. Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, fixed point theorems of multivalued maps, and generalized Clarke subdifferential, we show the existence of mild solutions for the fractional stochastic systems. Then we establish adequate conditions to guarantee the exponential decay of the mild solution towards zero in the square mean. Next, our results cover problems involving optimal control. Finally, we present theoretical application to support the validity of the study.