Abstract
In this manuscript, we initiate a study on a class of stochastic fractional differential equations driven by Lévy noise. The existence and uniqueness theorem of solutions to equations of this class is established under global and local Carathéodory conditions. Our analysis makes use of the Carathéodory 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.
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