Study on a semilinear fractional stochastic system with multiple delays in control

Abstract

This paper studies a semilinear fractional stochastic differential equation with multiple constant point delays in control. We transform the controllability problem into a fixed point problem. We obtain sufficient condition for the controllability by using Schauder's fixed point theorem. In addition, we discuss the optimal controllability of the problem. Some examples are given to illustrate the main result.

Keywords

• caputo fractional derivative
• controllability
• stochastic system
• control
• multiple delays