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

Abstract

This work is devoted to establish the optimal solutions of optimal control problems for a class of fractional impulsive stochastic integro-differential inclusions with Rosenblatt process and infinite delay in Hilbert spaces. Firstly, using the fractional calculus, the measure of noncom-pactness, properties of fractional resolvent operators and a fixed-point theorem, the existence of mild solutions for these systems is presented. Secondly, the existence of approximate solutions of optimal control problems without the hypotheses of compactness is also obtained. Finally, two examples are given to show applicability of our results. 2020 MR Subject Classification: 34A37; 60H15; 34K50; 26A33; 93E20