Existence and uniqueness of solutions of nonlinear fractional stochastic differential systems with nonlocal functional boundary conditions

Abstract

The authors study the existence and uniqueness of solutions to nonlinear first-order fractional stochastic differential systems driven by Brownian motion and with nonlocal functional boundary conditions. The technique of proof involves Perov’s fixed point theorem with matrices that converge to zero and the Leray–Schauder theorem.

Keywords:

• Fractional Brownian motion
• fixed point theorem
• mild solutions
• stochastic functional differential equation
• Brownian motion

AMS (MOS) Subject Classifications:

• 35R60
• 60H15
• 60G18
• 35A01

Acknowledgments

The authors would like to thank the anonymous referee for the careful reading of the manuscript and pertinent comments; the constructive suggestions substantially improved the quality of this work.

Disclosure statement

The authors report there are no competing interests to declare.