Averaging principle and stability of hybrid stochastic fractional differential equations driven by Lévy noise

Abstract

Stability of stochastic differential equations driven by Lévy noise with Markovian switching has recently received a lot of attention. Different from the integer-order stochastic differential equations, stochastic fractional differential equations play a circular role in describing many practical processes and systems. In this paper, our aims are to study the averaging principle of the solution of hybrid stochastic fractional differential equations driven by Lévy noise under non-Lipschitz conditions which include classical Lipschitz conditions as special cases and propose several sufficient conditions for asymptotic stability in the pth moment of the solution. Two examples with numerical simulation are given to illustrate the obtained theory.