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 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.

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 Inequalities and pth moment exponential stability of impulsive delayed Hopfield neural networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yutian Zhang ◽  
Guici Chen ◽  
Qi Luo
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
New Method ◽  
Integral Inequalities ◽  
Delay Function ◽  
Pth Moment Exponential Stability ◽  
Moment Exponential Stability

AbstractIn this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities. Our discussion neither requires a complicated Lyapunov function nor the differentiability of the delay function. In addition, we also summarize a new result on the exponential stability of a class of impulsive integral inequalities. Finally, one example is given to illustrate the effectiveness of the obtained results.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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