Conformable Fractional Stochastic Differential Inclusions Driven by Poisson Jumps with Optimal Control and Clarke Subdifferential

S. Varshini (), K. Ravikumar (), K. Ramkumar () and Hamdy M. Ahmed ()
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S. Varshini: Sri Eshwar College of Engineering
K. Ravikumar: PSG College of Arts & Science
K. Ramkumar: PSG College of Arts & Science
Hamdy M. Ahmed: El-Shorouk Academy

Journal of Theoretical Probability, 2025, vol. 38, issue 2, 1-26

Abstract: Abstract This manuscript is devoted to analysing the solvability and optimal control of a conformable fractional stochastic differential inclusion with Clarke subdifferential and deviated argument. The proposed conformable fractional impulsive inclusion system’s solvability in Hilbert space is established by employing fractional calculus, multivalued analysis, stochastic analysis, semigroup theory and a multivalued fixed point theorem. Furthermore, under some suitable assumptions, the existence of optimal control is derived by employing Balder’s theorem. Lastly, an application is provided to validate the developed theoretical results.

Keywords: Conformable fractional stochastic differential inclusion; Multivalued analysis; Optimal control; Poisson jumps; Deviated argument; 60H15; 34K40; 26A33; 34A08; 93B05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01414-z

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