Stability, boundedness, and square integrability of solutions to third order neutral differential equations with delay

2019 ◽  
Vol 69 (3) ◽  
pp. 823-836
Author(s):  
Anes M. Khatir ◽  
John R. Graef ◽  
Moussadek Remili
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
Square Integrability ◽  
Equations With Delay

scholarly journals Boundedness and oscillation of third order neutral differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Božena Mihalíková ◽  
Eva Kostiková
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
The Relationship ◽  
Oscillation Of Solutions

Abstract The relationship between boundedness and oscillation of solutions of the third order neutral differential equations are presented.

scholarly journals On Local Generalized Ulam–Hyers Stability for Nonlinear Fractional Functional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Dongming Nie ◽  
Azmat Ullah Khan Niazi ◽  
Bilal Ahmed
Keyword(s):  
Differential Equations ◽  
Existence Of A Solution ◽  
Neutral Differential Equations ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Functional Differential ◽  
Schauder Theorem ◽  
Equations With Delay ◽  
Rassias Stability ◽  
Fractional Functional

We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray–Schauder theorem, Arzela–Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam–Hyers stability and local generalized Ulam–Hyers–Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.

scholarly journals Oscillation Criteria of Third-Order Nonlinear Impulsive Differential Equations with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xiuxiang Liu
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Third Order ◽  
Oscillation Criteria ◽  
Impulsive Equations ◽  
Equations With Delay

This paper deals with the oscillation of third-order nonlinear impulsive equations with delay. The results in this paper improve and extend some results for the equations without impulses. Some examples are given to illustrate the main results.

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