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On a Ψ -Caputo-type fractional Stochastic Differential Equation |
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PP: 393-399 |
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doi:10.18576/pfda/080304
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Author(s) |
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McSylvester Ejighikeme Omaba,
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Abstract |
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| Consider a Ψ –Caputo fractional stochastic differential equation of order 0 < ν < 1 given by CDν,Ψ φ(x,t) = γ θ(φ(y,t))w ̇(y,t)dy, t > 0.
0 B(0,tν)
Assume a non-negative and bounded function φ (x, 0) = φ0 (x), x ∈ B(0, t ν ) ⊂ R2 , C D ν ,Ψ is a generalized Ψ –Caputo fractional ν0
derivative operator, θ : B(0,t ) → R is Lipschitz continuous, w ̇(y,t) a space-time white noise and γ > 0 the noise level. Under some
http://dx.doi.org/10.18576/pfda/080304
precise conditions, we present the existence and uniqueness of solution to the class of equation and give upper moment growth bound
and the long-term behaviour of the mild solution for the parameter ν such that 1 < ν < 1. The result shows that the second moment of 2
the solution to the Ψ–Caputo-type fractional stochastic differential equation exhibits an exponential growth in time at most c expc γ 2 Ψ(t), ∀t > 0; and at a rate of 2 as the noise level grows large.
5 6 2ν−1 2ν−1
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