Asymptotic behaviour of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation

Erkan Nane, Eze R. Nwaeze and McSylvester Ejighikeme Omaba

Statistics & Probability Letters, 2020, vol. 163, issue C

Abstract: Consider the following class of conformable time-fractional stochastic equation, for any x∈R fixed, Tα,tau(x,t)=λσ(u(x,t))Ẇt,t∈[a,∞),0<α<1, with a non-random initial condition u(x,0)=u0(x),x∈R assumed to be non-negative and bounded, Tα,ta is a conformable time-fractional derivative, σ:R→R is globally Lipschitz continuous, Ẇt a generalized derivative of Wiener process and λ>0 is the noise level. Given some precise and suitable conditions on the non-random initial function, we study the asymptotic behaviour of the solution with respect to the time parameter t and the noise level parameter λ. We also show that when the non-linear term σ grows faster than linear, the energy of the solution blows-up at finite time for all α∈(0,1).

Keywords: Asymptotic behaviour; Conformable time-fractional derivative; Moment growth bounds; Global non-existence; Stochastic equation; Stochastic Volterra type equation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spl.2020.108792

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