Averaging principle for fractional stochastic differential equations driven by Rosenblatt process and Poisson jumps

This manuscript addresses the averaging principle for Riemann-Liouville fractional stochastic differential equations with delays, driven by both the Rosenblatt process and Poisson jumps. Assumptions are made based on the Lipschitz condition, growth condition and averaging condition. Using Cauchy's, Doob's martingale and Gronwall-Bellman inequalities, the solution to the averaged autonomous system is derived, which approximates the solution to the proposed nonautonomous system in the mean square sense. Numerical simulation is provided to understand the obtained results.