On a Nonlinear Fractional Langevin Equation of Two Fractional Orders with a Multiplicative Noise

نویسندگان

چکیده

We consider a stochastic nonlinear fractional Langevin equation of two orders Dβ(Dα+γ)ψ(t)=λϑ(t,ψ(t))w˙(t),0<t≤1. Given some suitable conditions on the above parameters, we prove existence and uniqueness mild solution to initial value problem for using Banach fixed-point theorem (Contraction mapping theorem). The upper bound estimate second moment is given, which shows exponential growth in time t at precise rate 3c1expc3t2(α+β)−1+c4t2α−1 parameters α>1 α+β>1 positive constants c1,c3 c4.

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ژورنال

عنوان ژورنال: Fractal and fractional

سال: 2022

ISSN: ['2504-3110']

DOI: https://doi.org/10.3390/fractalfract6060290