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

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.