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Fractional time stochastic partial differential equations

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  • Chen, Zhen-Qing
  • Kim, Kyeong-Hun
  • Kim, Panki

Abstract

In this paper, we introduce a class of stochastic partial differential equations (SPDEs) with fractional time-derivatives, and study the L2-theory of the equations. This class of SPDEs can be used to describe random effects on transport of particles in medium with thermal memory or particles subject to sticking and trapping.

Suggested Citation

  • Chen, Zhen-Qing & Kim, Kyeong-Hun & Kim, Panki, 2015. "Fractional time stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1470-1499.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1470-1499
    DOI: 10.1016/j.spa.2014.11.005
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    References listed on IDEAS

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    1. Guido Germano & Mauro Politi & Enrico Scalas & Ren'e L. Schilling, 2008. "Stochastic calculus for uncoupled continuous-time random walks," Papers 0802.3769, arXiv.org, revised Jan 2009.
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    Cited by:

    1. Junmei Wang & James Hoult & Yubin Yan, 2021. "Spatial Discretization for Stochastic Semi-Linear Subdiffusion Equations Driven by Fractionally Integrated Multiplicative Space-Time White Noise," Mathematics, MDPI, vol. 9(16), pages 1-38, August.
    2. Kumar, Vivek, 2022. "Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise," Statistics & Probability Letters, Elsevier, vol. 184(C).
    3. Chen, Le & Hu, Yaozhong & Nualart, David, 2019. "Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5073-5112.
    4. Zou, Guang-an & Lv, Guangying & Wu, Jiang-Lun, 2018. "On the regularity of weak solutions to space–time fractional stochastic heat equations," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 84-89.
    5. Asogwa, Sunday A. & Nane, Erkan, 2017. "Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1354-1374.
    6. Tuan, Nguyen Huy & Caraballo, Tomás & Thach, Tran Ngoc, 2023. "New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 24-67.
    7. Liu, Xinfei & Yang, Xiaoyuan, 2023. "Numerical approximation of the stochastic equation driven by the fractional noise," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    8. Sweilam, N.H. & El-Sakout, D.M. & Muttardi, M.M., 2020. "Numerical study for time fractional stochastic semi linear advection diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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