scholarly journals Stability of a Class of Impulsive Neutral Stochastic Functional Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yue Liu ◽  
Dehao Ruan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Exponential Stability ◽  
Partial Differential ◽  
The Fixed Point Theorem ◽  
Moment Exponential Stability ◽  
Stochastic Functional

In this paper, a class of impulsive neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion is investigated. Under some suitable assumptions, the pth moment exponential stability is discussed by means of the fixed-point theorem. Our results also improve and generalize some previous studies. Moreover, one example is given to illustrate our main results.

scholarly journals Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal ◽  
Ahmed Kajouni
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Cauchy Problems ◽  
Partial Differential ◽  
Krasnoselskii’S Fixed Point Theorem

In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.

scholarly journals The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Dehao Ruan ◽  
Jiaowan Luo
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Fixed Point Method ◽  
Standard Brownian Motion ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

We focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach fixed point method. Moreover, an example is presented to illustrate our main results.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

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