scholarly journals On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-26 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Stochastic Analysis ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Approximation Techniques ◽  
Approximately Controllable ◽  
Stochastic Functional

We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

scholarly journals Existence of Second Order Impulsive Neutral Integro-Differential Evolution Control Systems with an Infinite Delay

2019 ◽  
Vol 8 (3) ◽  
pp. 8857-8862
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive neutral integrodifferential evolution systems with an infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Differential Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
P. Palani ◽  
T. Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Bounded Linear ◽  
Cosine Families ◽  
Differential Control

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
Perumal Palani ◽  
Tharmalingam Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive partial neutral evolution systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Periodic Solutions of Second Order Degenerate Differential Equations with Delay in Banach Spaces

2018 ◽  
Vol 61 (4) ◽  
pp. 717-737 ◽  
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Order Degenerate ◽  
Degenerate Differential Equations ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Closed Linear Operators

AbstractWe give necessary and sufficient conditions of the Lp-well-posedness (resp. -wellposedness) for the second order degenerate differential equation with finite delayswith periodic boundary conditions (Mu)(0) = (Mu)(2π), (Mu)′ (0) = (Mu)′ (2π), where A, B, and M are closed linear operators on a complex Banach space X satisfying D(A) ∩ D(B) ⊂ D(M), F and G are bounded linear operators from into X.

Approximate Controllability of Partial Fractional Neutral Integro-Differential Inclusions With Infinite Delay in Hilbert Spaces

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Zuomao Yan ◽  
Hongwu Zhang
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Approximately Controllable ◽  
Fractional System ◽  
The Fixed Point Theorem ◽  
Necessary And Sufficient

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the 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 Approximate controllability of semi-linear stochastic integro-differential equations with infinite delay

2020 ◽  
Vol 37 (4) ◽  
pp. 1133-1167
Author(s):  
Hai Huang ◽  
Xianlong Fu
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fundamental Solutions ◽  
Resolvent Operators ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Approximately Controllable

Abstract In this work, by constructing fundamental solutions and using the theory of resolvent operators and fractional powers of operators, we study the approximate controllability of a class of semi-linear stochastic integro-differential equations with infinite delay in $L_p$ space ($2<p<\infty $). Sufficient conditions for approximate controllability of the discussed equations are obtained under the assumption that the associated deterministic linear system is approximately controllable. An example is provided to illustrate the obtained results.

scholarly journals Holder's Inequality ρ–Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Sameer Qasim Hasan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Infinite Delay ◽  
Hölder’S Inequality ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Operators ◽  
Bounded Linear ◽  
Hölder's Inequality

We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder’s fixed point theorem with Holder’s inequality ρ–mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point.

Asymptotic behavior of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2727-2748
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Asymptotic Behavior ◽  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Lipschitz Continuous ◽  
Stochastic Functional

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

scholarly journals Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Dang Huan Diem
Keyword(s):  
Infinite Delay ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Bounded Linear ◽  
Infinite Delays ◽  
Strongly Continuous Cosine Family

The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given.

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