Abstract: In this paper, we discuss the stability with general decay rate of neutral stochastic fractional hybrid differential equations driven by Lévy noise. By using Lyapunov function, nonnegative semi-martingale convergence theorem and the theory of M-matrix, we propose sufficient conditions for the almost sure stability. We also give an upper bound of each coefficient at any state.

Key words: stochastic fractional differential equations, nonnegative semi-martingale convergence, Lévy noise