scholarly journals On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise inℝd

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xichao Sun ◽  
Zhi Wang ◽  
Jing Cui
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Arbitrary Dimension ◽  
Derivative Operator ◽  
Fractional Noise ◽  
Fixed Point Principle ◽  
Whole Space

We study a stochastic partial differential equation in the whole spacex∈ℝd, with arbitrary dimensiond≥1, driven by fractional noise and a pure jump Lévy space-time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.

scholarly journals Controllability of semilinear stochastic evolution equations in Hilbert space

2001 ◽  
Vol 14 (4) ◽  
pp. 329-339 ◽  
Author(s):  
P. Balasubramaniam ◽  
J. P. Dauer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Evolution Equations ◽  
Stochastic Partial Differential Equation ◽  
Semigroup Theory ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

Controllability of semilinear stochastic evolution equations is studied by using stochastic versions of the well-known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation is given.

scholarly journals Inverse problem of determining the coefficient and kernel in an integro - differential equation of parabolic type

2021 ◽  
Author(s):  
Zhonibek Zhumaev ◽  
Durdimurod Durdiev
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Parabolic Type ◽  
Differential Heat ◽  
Inverse Boundary ◽  
Fixed Point Principle ◽  
Uniqueness Of A Solution

This article is concerned with the study of the unique solvability of inverse boundary value problem for integro-differential heat equation. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown.

scholarly journals Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Dengfeng Xia ◽  
Litan Yan ◽  
Weiyin Fei
Keyword(s):  
Fixed Point ◽  
Heat Equation ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Fractional Laplacian ◽  
Brownian Sheet ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Fixed Point Principle ◽  
Uniqueness Of The Solution

We consider the stochastic heat equation of the form∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H,whereW˙His the fractional noise,L˙is a (pure jump) Lévy space-time white noise,Δis Laplacian, andΔα=-(-Δ)α/2is the fractional Laplacian generator onR, andf,σ:[0,T]×R×R→Rare measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.

MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (02) ◽  
pp. 271-294 ◽  
Author(s):  
B. BOUFOUSSI ◽  
N. MRHARDY
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Yosida Approximation ◽  
Partial Differential ◽  
Doubly Stochastic ◽  
Uniqueness Of The Solution

In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.

scholarly journals Mild Solution for a Stochastic Partial Differential Equation with Noise

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
White Noise ◽  
Mild Solution ◽  
Point Theorem ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Equation ◽  
Multiplicative White Noise

This paper focuses on the study of the existence of a mild solution to time and space-fractional stochastic equation perturbed by multiplicative white noise. The required results are obtained by means of Sadovskii’s fixed point theorem.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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