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 of Impulsive Fractional Functional Integro-Differential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
C. Ravichandran ◽  
J. J. Trujillo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Mixed Type ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Controllability Result ◽  
Fractional Functional

This paper is concerned with the controllability problem for a class of mixed type impulsive fractional integro-differential equations in Banach spaces. Sufficient conditions for the controllability result are established by using suitable fixed point theorem combined with the fractional calculus theory and solution operator under some weak conditions. The example is given in illustrate the theory. The results of this article are generalization and improved of the recent results on this issue.

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.

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 Existence and Controllability Results for Mixed Functional Integrodifferential Equations with Infinite Delay

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Kishor D. Kucche
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Integrodifferential Equations ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Controllability Result

AbstractSufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.

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.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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.

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.

Approximate controllability of semilinear impulsive functional differential systems with non-local conditions

2020 ◽  
Vol 37 (4) ◽  
pp. 1070-1088 ◽  
Author(s):  
Sumit Arora ◽  
Soniya Singh ◽  
Jaydev Dabas ◽  
Manil T Mohan
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Local Conditions ◽  
Functional Differential Systems ◽  
Non Local ◽  
Functional Differential

Abstract This paper is concerned with the approximate controllability of semilinear impulsive functional differential systems in Hilbert spaces with non-local conditions. We establish sufficient conditions for approximate controllability of such systems via resolvent operator and Schauder’s fixed point theorem. An application involving the impulse effect associated with delay and non-local conditions is presented to verify our claimed results.

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