Stochastic exponential stabilization and optimal control results for a class of fractional order equations

• Published in: Chaos, solitons and fractals Vol. 185; p. 115087
• Main Authors: Dineshkumar, Chendrayan, Jeong, Jae Hoon, Joo, Young Hoon
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2024
• Subjects: Approximate controllability; Exponential stability; Fractional derivative; Impulsive equation; Optimal control; Poisson jumps; Sectorial operators; 37L55; Approximate controllability; 26A33; Impulsive equation; Exponential stability; Fractional derivative; 93D23; Sectorial operators; 47B12; 93B05; Optimal control; Poisson jumps; 35R12
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2024.115087

The object of this study is to define existence, controllability and exponential stability results within a Sobolev-type fractional stochastic neutral equations of order 1<ω<2 with sectorial operator and optimal control. To do this, first, this study relies on the confluence of stochastic analysis, fractional calculus, sectorial operator, and the applicability of Sadovskii’s fixed point method. First, we highlight the existence of mild solutions to the fractional stochastic control equation and then introduce the concept of approximate controllability. Next, employing an impulsive Poisson system yields sufficient conditions for guaranteeing the exponential stability of the mild solution in the mean square moment. Further, our inquiry expands into the existence of optimal control. Finally, an example is provided to illustrate the obtained theory. •This paper explores the stability of the fractional delay system of order ω∈(1,2).•This paper is the first study of a fractional jumps system with sectorial operators.•We establish conditions for the fractional system and extend to the controllability.•We determine mean square stability of fractional system ω∈(1,2) with Poisson jumps.•Finally, an optimal control pair is provided to show the solvability of the problem.