Stochastic fractional differential equations driven by Levy noise under Caratheodory conditions

In this manuscript, we initiate a study on a class of stochastic fractional differential equations driven by Levy noise. The existence and uniqueness theorem of solutions to equations of this class is established under global and local Caratheodory conditions. Our analysis makes use of the Caratheodory approximation as well as a stopping time technique. The results obtained here generalize the main results from Pedjeu and Ladde [Chaos, Solitons Fractals 45, 279-293 (2012)], Xu et al. [Appl. Math. Comput. 263, 398-409 (2015)], and Abouagwa et al. [Appl. Math. Comput. 329, 143-153 (2018)]. Finally, an application to the stochastic fractional Burgers differential equations is designed to validate the theory obtained.