scholarly journals The Neutral Stochastic Integrodifferential Equations with Jumps

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Diem Dang Huan
Keyword(s):  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
Initial Value ◽  
Carathéodory Conditions ◽  
Global And Local ◽  
Continuous Dependence Of Solutions

We study the existence and uniqueness of mild solutions for neutral stochastic integrodifferential equations with Poisson jumps under global and local Carathéodory conditions on the coefficients by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value. Finally, an example is provided to illustrate the effectiveness of the obtained results.

scholarly journals Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Mamadou Abdoul Diop ◽  
Khalil Ezzinbi ◽  
Modou Lo
Keyword(s):  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Integrodifferential Equations

This paper presents the result on existence, uniqueness of mild solutions to neutral stochastic partial functional integrodifferential equations under the Carathéodory-type conditions on the coefficients. The results are obtained by using the method of successive approximation. An example is provided to illustrate the results of this work.

scholarly journals Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Fathalla A. Rihan ◽  
Chinnathambi Rajivganthi ◽  
Palanisamy Muthukumar
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Poisson Jumps ◽  
Hilfer Fractional Derivative ◽  
Analysis Techniques ◽  
Mild Conditions ◽  
Fractional Stochastic Differential Equations ◽  
Existence Of Optimal Control

In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

THE EXISTENCE AND UNIQUENESS FOR NON-LIPSCHITZ STOCHASTIC NEUTRAL DELAY EVOLUTION EQUATIONS DRIVEN BY POISSON JUMPS

2009 ◽  
Vol 09 (01) ◽  
pp. 135-152 ◽  
Author(s):  
JIAOWAN LUO ◽  
TAKESHI TANIGUCHI
Keyword(s):  
Existence And Uniqueness ◽  
Initial Function ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Processes ◽  
Poisson Jumps ◽  
Neutral Delay ◽  
Poisson Jump

In this paper, we consider the existence and uniqueness of mild solutions to non-Lipschitz stochastic neutral delay evolution equations driven by Poisson jump processes: [Formula: see text] with an initial function X(s) = φ(s), -r ≤ s ≤ 0, where φ : [-r, 0] → H is a cadlag function with [Formula: see text].

scholarly journals Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongxia Fan ◽  
Yongxiang Li ◽  
Pengyu Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Elastic System ◽  
Mild Solutions ◽  
Structural Damping ◽  
Initial Value ◽  
Operator Semigroups ◽  
Elastic Systems ◽  
Theoretical Results

This paper deals with the existence and uniqueness of mild solutions for a second order evolution equation initial value problem in a Banach space, which can model an elastic system with structural damping. The discussion is based on the operator semigroups theory and fixed point theorem. In addition, an example is presented to illustrate our theoretical results.

scholarly journals Existence and Compactness Results for a System of Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Cheikh Guendouz ◽  
Jamal Eddine Lazreg ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Solution Sets ◽  
Fractional Differential ◽  
Continuous Dependence Of Solutions

The existence and uniqueness, boundedness, and continuous dependence of solutions for fractional differential equations with Caputo fractional derivative is proven by Perov’s fixed point theorem in vector Banach spaces. We study the existence and compactness of solution sets and the u.s.c. of operator solutions.

scholarly journals Prevalence of backward stochastic differential equations with unique solution

2004 ◽  
Vol 2004 (2) ◽  
pp. 123-136
Author(s):  
K. Bahlali ◽  
B. Mezerdi ◽  
Y. Ouknine
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Baire Category ◽  
Backward Stochastic Differential Equations ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Almost All ◽  
Continuous Dependence Of Solutions

We prove that in the sense of Baire category, almost all backward stochastic differential equations (BSDEs) with bounded and continuous coefficient have the properties of existence and uniqueness of solutions as well as the continuous dependence of solutions on the coefficient and the L2-convergence of their associated successive approximations.

Sign in / Sign up

Export Citation Format

Share Document