Time Optimal Control of System Governed by a Fractional Stochastic Partial Differential Inclusion with Clarke Subdifferential

Abstract

This paper investigates the time optimal control problems to a new class of fractional non-instantaneous impulsive stochastic partial differential inclusions with Clarke subdifferential in Hilbert spaces. Firstly, using the fractional calculus, properties of fractional resolvent operators and a fixed-point theorem, the existence of mild solutions for these systems is presented. Secondly, the existence of time optimal control of system governed by fractional stochastic control inclusions with Clarke subdifferential and non-instantaneous impulses is also obtained. Finally, an example is given to illustrate our main results.

Approximate solutions of optimal control problems for a fractional stochastic integro-differential inclusion with Rosenblatt process

“…Durga et al [18] investigated the optimal control of a class of non-instantaneous impulsive Sobolev-type fractional stochastic differential inclusion involving Poisson jumps and Clarke subdifferential. The time optimal control problems of fractional noninstantaneous impulsive stochastic partial differential inclusions with Clarke subdifferential in Hilbert spaces is studied [19]. These systems driven by Brownian motion or fractional Brownian motion.…”