Hyers-Ulam Rassias Stability of a Second Order Delay Differential Equation

Year 2018, Volume: 8 Issue: 2, 249 - 254, 31.07.2018

Emel Biçer

https://doi.org/10.17714/gumusfenbil.350309

Abstract

In this study, firstly, we
use Banach fixed point theorem to show that the Hyers-Ulam Rassias stability of
a first order delay differential equation with constant delay of the form

where is continuous function and  is a nonnegative real
constant. By taking advantage of this result, we investigate Hyers-Ulam Rassias
stability of a second order delay differential equation with constant delay of
the form

where  are continuous
functions and  is a nonnegative real
constant. Also we present an example to illustrate the theoretical analysis.

Keywords

Banach Fixed Point Theorem, Delay Differential Equation, Hyers-Ulam Rassias Stability

İkinci Mertebeden Gecikmeli Bir Diferansiyel Denklemin Hyers-Ulam Rassias Kararlılığı

Abstract

Bu çalışmada, ilk olarak  bir sürekli fonksiyon
ve  negatif olmayan reel
bir sabit olmak üzere

,

şeklindeki birinci mertebeden sabit gecikmeli bir diferansiyel denklemin Banach
sabit nokta teoremi kullanılarak Hyers-Ulam Rassias kararlılığı gösterildi.
Buradan elde edilen sonuçtan faydalanılarak  sürekli fonksiyonlar
olmak üzere

biçimindeki ikinci mertebeden sabit gecikmeli bir diferansiyel denklemin
Hyers-Ulam Rassias kararlılığı araştırıldı. Ayrıca çalışmadaki teorik
analizleri açıklamak için bir örnek verildi. 

Keywords

Banach Sabit Nokta Teoremi, Gecikmeli Diferansiyel Denklem, Hyers-Ulam Rassias Kararlılık

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