scholarly journals A new result on the global exponential stability of nonlinear neutral volterra integro-differential equation with variable lags

2020 ◽  
Vol 05 (01) ◽  
pp. 29-43
Author(s):  
Yener Altun
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Integro Differential Equation

GLOBAL EXPONENTIAL STABILITY FOR A CLASS OF IMPULSIVE INTEGRO-DIFFERENTIAL EQUATION

2008 ◽  
Vol 18 (03) ◽  
pp. 735-743 ◽  
Author(s):  
QINGHUA ZHOU
Keyword(s):  
Differential Equation ◽  
Exponential Stability ◽  
Spectral Radius ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Integro Differential Equation ◽  
Dynamical Behaviors ◽  
Theoretical Results

The convergent dynamical behaviors of a class of impulsive integro-differential equation are discussed. By establishing an integro-differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of non-negative matrices, some new sufficient conditions to guarantee the global exponential stability are obtained. The results extend and improve the earlier publications. An example is given to illustrate the theoretical results.

scholarly journals Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Youssef Raffoul ◽  
Habib Rai
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exponential Stability ◽  
Lyapunov Functional ◽  
Infinite Delay ◽  
Zero Solution ◽  
Uniform Stability ◽  
Lyapunov Functionals ◽  
Integro Differential Equation ◽  
The Stability

AbstractIn [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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