An averaging result for fractional variable-order neutral differential equations with variable delays driven by Markovian switching and Lévy noise

In this paper, we derive new results on the averaging principle for a class of Caputo neutral stochastic system driven by Markovian switching and L & eacute;vy noise with variable delays and time-varying fractional order. Under a set of appropriate conditions, we showed that solutions of the averaged stochastic systems approach the solutions of the original stochastic systems in the sense of both convergences in mean square and convergence in probability. Finally, we attach two examples with numerical simulations to justify the validity of our theory.