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.
منابع مشابه
Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses
*Correspondence: [email protected] 2Department of Mathematics, China University of Petroleum, Qingdao, Shandong 266555, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we study a new type of a Langevin equation involving two different fractional orders and impulses. Sufficient conditions are formulated for the existence and uniqueness ...
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ژورنال
عنوان ژورنال: Fractal and fractional
سال: 2022
ISSN: ['2504-3110']
DOI: https://doi.org/10.3390/fractalfract6060290