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Regularity of fractional stochastic convolution and its application to fractional stochastic chaotic systems

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  • Huang, Xiuqi
  • Wang, Xiangjun

Abstract

The current paper is devoted to the regularity of Caputo-type fractional Onstein–Ulenbeck processes with fractional Brownian motion, and it is applied to establish the existence and uniqueness of the mild solution for Caputo-type fractional Rössler equation and fractional Chen equation with fractional Brownian motion. Some numerical simulations and examples are provided to support the theoretical results.

Suggested Citation

  • Huang, Xiuqi & Wang, Xiangjun, 2021. "Regularity of fractional stochastic convolution and its application to fractional stochastic chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:chsofr:v:149:y:2021:i:c:s096007792100401x
    DOI: 10.1016/j.chaos.2021.111047
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    References listed on IDEAS

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    1. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    2. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    3. Xu, Pengfei & Huang, Jianhua & Zeng, Caibin, 2020. "Ergodicity of stochastic Rabinovich systems driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    4. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
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