Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Youssef Benkabdi ◽  
E. Lakhel
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Stochastic Analysis ◽  
Separable Hilbert Space ◽  
Infinite Delay ◽  
Abstract Result ◽  
Differential Systems ◽  
Unbounded Delay ◽  
Rosenblatt Process ◽  
Controllability Result

Abstract In this paper, the controllability of a class of impulsive neutral stochastic integro-differential systems with infinite delay driven by Rosenblatt process in a separable Hilbert space is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. A practical example is provided to illustrate the viability of the abstract result of this work.

scholarly journals Controllability of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion with delay and Poisson jumps

2021 ◽  
Author(s):  
Youssef Benkabdi ◽  
Lakhel El Hassan
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stochastic Analysis ◽  
Separable Hilbert Space ◽  
Infinite Delay ◽  
Poisson Jumps ◽  
Differential Systems ◽  
Controllability Result

In this paper the controllability of a class of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in a separable Hilbert space with infinite delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

scholarly journals Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Jing Cui
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Abstract Space ◽  
Differential Systems ◽  
Compactness Condition ◽  
Fixed Point Principle ◽  
Controllability Result

This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

scholarly journals Controllability for neutral stochastic functional integrodifferential equations with infinite delay

2016 ◽  
Vol 1 (2) ◽  
pp. 493-506 ◽  
Author(s):  
Tomás Caraballo ◽  
Mamadou Abdoul Diop ◽  
Aziz Mane
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Separable Hilbert Space ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Resolvent Operators ◽  
Real Separable Hilbert Space ◽  
Stochastic Functional

AbstractIn this work, we study the controllability for a class of nonlinear neutral stochastic functional integrodifferential equations with infinite delay in a real separable Hilbert space. Sufficient conditions for the controllability are established by using Nussbaum fixed point theorem combined with theories of resolvent operators. As an application, an example is provided to illustrate the obtained result.

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Approximately Controllable ◽  
Fractional Neutral Evolution Equations

We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using Krasnoselkii's fixed-point theorem, fractional calculus, and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional neutral differential equations with infinite delay are formulated and proved. The results of the paper are generalization and continuation of the recent results on this issue.

scholarly journals A common unique fixed point theorem for two random operators in Hilbert spaces

2002 ◽  
Vol 32 (3) ◽  
pp. 177-182 ◽  
Author(s):  
Binayak S. Choudhury
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Hilbert Spaces ◽  
Closed Subset ◽  
Separable Hilbert Space ◽  
Unique Fixed Point ◽  
Random Operators ◽  
Nonempty Closed Subset ◽  
Random Fixed Point

We construct a sequence of measurable functions and consider its convergence to the unique common random fixed point of two random operators defined on a nonempty closed subset of a separable Hilbert space. The corresponding result in the nonrandom case is also obtained.

Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yousef Alnafisah ◽  
Hamdy M. Ahmed
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Point Theorem ◽  
Stochastic Analysis ◽  
Sufficient Conditions ◽  
Null Controllability ◽  
Integrodifferential System ◽  
Rosenblatt Process ◽  
Poisson Jump

Abstract In this paper, we investigate the sufficient conditions for null controllability of noninstantaneous impulsive Hilfer fractional stochastic integrodifferential system with the Rosenblatt process and Poisson jump. The required results are obtained based on fractional calculus, stochastic analysis, and Sadovskii’s fixed point theorem. Finally, an example is given to illustrate the obtained results.

EXISTENCE AND CONTROLLABILITY RESULTS FOR INFINITE DELAY PARTIAL FUNCTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-VALUED IMPULSES IN BANACH SPACES

2010 ◽  
Vol 03 (04) ◽  
pp. 631-646 ◽  
Author(s):  
Hanwen Ning ◽  
Bing Liu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

This paper is concerned with the existence and controllability of solutions for infinite delay functional differential systems with multi-valued impulses in Banach space. Sufficient conditions for the existence are obtained by using a fixed point theorem for multi-valued maps due to Dhage. An example is also given to illustrate our results.

scholarly journals The Carathéodory–Cartan–Kaup–Wu Theorem on an Infinite-Dimensional Hilbert Space

2007 ◽  
Vol 185 ◽  
pp. 17-30 ◽  
Author(s):  
Joseph A. Cima ◽  
Ian Graham ◽  
Kang Tae Kim ◽  
Steven G. Krantz
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Bounded Domain ◽  
Separable Hilbert Space ◽  
Holomorphic Mappings ◽  
Rigidity Result ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Main Technique ◽  
Dimensional Version

AbstractThis paper treats a holomorphic self-mapping f: Ω → Ω of a bounded domain Ω in a separable Hilbert space with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the Cartan-Carathéodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. Cartan, is iteration of the mapping f and its derivative. A normality result for holomorphic mappings in the compact-weak-open topology, due to Kim and Krantz, is used.

scholarly journals Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xisheng Dai ◽  
Feng Yang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Complete Controllability ◽  
Differential Systems ◽  
Stochastic Wave Equation

This paper concerns the complete controllability of the impulsive stochastic integrodifferential systems in Hilbert space. Based on the semigroup theory and Burkholder-Davis-Gundy's inequality, sufficient conditions of the complete controllability for impulsive stochastic integro-differential systems are established by using the Banach fixed point theorem. An example for the stochastic wave equation with impulsive effects is presented to illustrate the utility of the proposed result.

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