η-Stability for stochastic functional differential equation driven by time-changed Brownian motion

Abstract

Abstract This manuscript focuses on a class of stochastic functional differential equations driven by time-changed Brownian motion. By utilizing the Lyapunov method, we capture some sufficient conditions to ensure that the solution for the considered equation is η-stable in the pth moment sense. Subsequently, we present some new criteria of the η-stability in mean square by using time-changed Itô formula and proof by contradiction. Finally, we provide some examples to demonstrate the effectiveness of our main results.

Keywords

• h-stability
• Time-changed Brownian motion
• Lyapunov method
• Time-changed Itô formula