CONTROLLABILITY OF NONLINEAR HIGHER-ORDER FRACTIONALDAMPED STOCHASTIC SYSTEMS INVOLVING MULTIPLE DELAYS

Abstract

This paper is concerned with the controllability problem for higher-order fractionaldamped stochastic systems with multiple delays, which involves fractional Caputo derivatives ofany different orders. In the process of proof, we have proposed the controllability of consideredlinear system by establishing a controllability Grammian matrix and employing a control function.Sufficient conditions for the considered nonlinear system concerned to be controllable have beenderived by constructing a proper control function and utilizing the Banach fixed point theoremwith Burkholder–Davis–Gundy’s inequality. Finally, two examples are provided to emphasize theapplicability of the derived results