On the existence and continuity of solutions to fractional stochastic differential equations in the framework of G-Lévy jumps

This study investigates the existence and uniqueness of solutions to fractional stochastic differential equations incorporating G-Lévy jumps. The theoretical framework is established by employing the Mittag-Leffler function, a generalized form of Gronwall’s inequality and the Picard approximation technique. The boundedness of exact solutions and Picard approximate solutions has been derived. Error estimates between the approximate solutions and the actual solutions are established. Additionally, the continuous dependence of solutions on initial values is explored. The Hölder’s continuity of the solutions is rigorously established. To demonstrate the practical relevance of the theoretical findings, a detailed example is provided.