scholarly journals Exponential stability of impulsive neutral stochastic integrodifferential equations driven by a poisson jumps and time-varying delays

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1809-1819
Author(s):  
A. Anguraj ◽  
K. Ravikumar ◽  
E.M. Elsayed
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Mild Solution ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Time Varying ◽  
Mean Square ◽  
Resolvent Operators ◽  
Poisson Jumps

The purpose of this work is to study the impulsive neutral stochastic integrodifferential equations driven by a Poisson jumps and time-varying delays. We use the theory of resolvent operators developed in Grimmer the prove an existence, uniqueness and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point theory. Finally, an illustrative example is given to demonstrate the effectiveness of the results.

scholarly journals Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed Point Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Tianxiang Yao ◽  
Xianghong Lai
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Stability Study ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square

This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.

Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps

2020 ◽  
Vol 21 (7-8) ◽  
pp. 727-737
Author(s):  
Subramaniam Saravanakumar ◽  
Pagavathigounder Balasubramaniam
Keyword(s):  
Fixed Point ◽  
Differential System ◽  
Approximate Controllability ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Resolvent Operators ◽  
Poisson Jumps ◽  
Controllability Problem ◽  
Rosenblatt Process ◽  
Analytic Resolvent

AbstractThis manuscript is concerned with the approximate controllability problem of Hilfer fractional stochastic differential system (HFSDS) with Rosenblatt process and Poisson jumps. We derive the main results in stochastic settings by employing analytic resolvent operators, fractional calculus and fixed point theory. Further, we express the theoretical result with an example.

scholarly journals Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

1991 ◽  
Vol 4 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Third Order ◽  
Nonnegative Solutions ◽  
Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

scholarly journals pth Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xuetao Yang ◽  
Quanxin Zhu ◽  
Zhangsong Yao
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Heat Equations ◽  
Stochastic Heat Equations ◽  
Pth Moment Exponential Stability ◽  
Infinite State ◽  
Moment Exponential Stability ◽  
Nonlinear Hybrid

We are concerned with the exponential stability problem of a class of nonlinear hybrid stochastic heat equations (known as stochastic heat equations with Markovian switching) in an infinite state space. The fixed point theory is utilized to discuss the existence, uniqueness, andpth moment exponential stability of the mild solution. Moreover, we also acquire the Lyapunov exponents by combining the fixed point theory and the Gronwall inequality. At last, two examples are provided to verify the effectiveness of our obtained results.

scholarly journals Instantaneous and Noninstantaneous Impulsive Integrodifferential Equations in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Gaston M. N'Guérékata
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
The Resolvent Operator

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.

scholarly journals On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Said Melliani ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Uniqueness Results

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

scholarly journals Fixed Point and Asymptotic Analysis of Cellular Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xianghong Lai ◽  
Yutian Zhang
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Trivial Equilibrium ◽  
The Stability

We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time-varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.

Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamdy M. Ahmed ◽  
Mahmoud M. El-Borai ◽  
Mohamed E. Ramadan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Fractional Brownian Motion ◽  
Mild Solution ◽  
Stochastic Analysis ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
New Class

AbstractIn this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

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