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Stochastic fractional differential equations driven by Lévy noise under Carathéodory conditions. (English) Zbl 1418.60051

Summary: 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 J.-C. Pedjeu and G. S. Ladde [Chaos, Solitons Fractals 45, 279–293 (2012; Zbl 1282.60058)], Y. Xu et al. [Appl. Math. Comput. 263, 398–409 (2015; Zbl 1410.60060)], and M. Abouagwa et al. [Appl. Math. Comput. 329, 143–153 (2018; doi:10.1016/j.amc.2018.02.005)]. Finally, an application to the stochastic fractional Burgers differential equations is designed to validate the theory obtained.{
©2019 American Institute of Physics}

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
60H40 White noise theory
34F05 Ordinary differential equations and systems with randomness
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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