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Space–time fractional stochastic partial differential equations

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  • Mijena, Jebessa B.
  • Nane, Erkan

Abstract

We consider non-linear time-fractional stochastic heat type equation ∂tβut(x)=−ν(−Δ)α/2ut(x)+It1−β[σ(u)W⋅(t,x)] in (d+1) dimensions, where ν>0,β∈(0,1), α∈(0,2] and d

Suggested Citation

  • Mijena, Jebessa B. & Nane, Erkan, 2015. "Space–time fractional stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3301-3326.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3301-3326
    DOI: 10.1016/j.spa.2015.04.008
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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    Cited by:

    1. Beghin, Luisa, 2018. "Fractional diffusion-type equations with exponential and logarithmic differential operators," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2427-2447.
    2. 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.
    3. 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.
    4. McSylvester Ejighikeme Omaba & Hamdan Al Sulaimani, 2022. "On Caputo–Katugampola Fractional Stochastic Differential Equation," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    5. Omaba, McSylvester Ejighikeme, 2021. "Growth moment, stability and asymptotic behaviours of solution to a class of time-fractal-fractional stochastic differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. 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.
    7. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2022. "The Optical Solutions of the Stochastic Fractional Kundu–Mukherjee–Naskar Model by Two Different Methods," Mathematics, MDPI, vol. 10(9), pages 1-10, April.

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