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Stochastic fractional evolution equations with fractional brownian motion and infinite delay

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  • Xu, Liping
  • Li, Zhi

Abstract

In this paper, we consider a class of stochastic fractional evolution equations with infinite delay and a fractional Brownian motion in a Hilbert space. By the stochastic analysis technique, we establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz condition with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory.

Suggested Citation

  • Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:36-46
    DOI: 10.1016/j.amc.2018.04.060
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