In this work, we study a class of neutral stochastic functional differential equations driven by G-Brownian motion. We derive by variation-of-constants formula sufficient conditions for exponential stability and quasi sure exponential stability of the solutions. Finally, we provide an example to illustrate the effectiveness of the theoretical results.

Some sufficient conditions for almost sure exponential stability of solutions to time-changed stochastic differential equations (SDEs) are presented. The principle technique of our investigation is to construct a proper Lyapunov function and carry out generalized Lyapunov methods to time-changed SDEs. In contrast to the almost sure exponential stability in existing articles, we present new results on the stability of solutions to time-changed SDEs. Finally, an example is given to demonstrate the effectiveness of our work.