Stability and continuity of solutions to fractional SDEs driven by G-Lévy jumps with non lipschitz conditions

This article investigates the mean square stability of solutions to fractional stochastic differential equations in the framework of G-Lévy processes. It has been established that the solutions within this framework exist and are unique. Error estimates have been thoroughly investigated, providing insights into the accuracy of the solutions. Furthermore, the regularity of solutions in the sense of Hölder continuity has been proven. The theoretical framework is developed under non-Lipschitz condition, employing the Mittag-Leffler function, a generalized Gronwall inequality, and BDG-type inequalities. With the inclusion of G-Lévy jumps, the space MGp(0,T) is no longer sufficient for deriving new results. To overcome this limitation, we utilize the space, HGp([0,T]×R0d) to address the associated challenges. Additionally, the solutions exhibit continuous dependence on the initial data. A detailed example is presented showing the applicability of the results.