Doğrusal olmayan kesirli fark denklemlerinin kararlılık analizi üzerine bir not: Karşılaştırmalı yaklaşım

Öz

Bu çalışmada ν∈(0,1] mertebesinde doğrusal olmayan kesirli fark denklemleri üzerinde durulmuş olup, h-kararlılık ve Mittag-Leffler kararlılığı kavramları kullanılarak bir kararlılık analizi yapılmıştır. Makalenin temel sonuçları odaklanılan kesirli fark denkleminin yardımcı bir kesirli fark denklemi ile karşılaştırılması ve kıyaslanması ile elde edilmiştir. Bu çalışmanın çıktıları literatürde kesirli denklemlerin kararlılık analizinde genellikle kullanılan sabit nokta teorisi ve Liapunov teorisi gibi araçların dışında bir yol kullanılarak elde edildiği için halen gelişmekte olan ayrık kesirli denklemlerin teorisine farklı bir bakış açısı sunarak katkı sağlamıştır.

Anahtar Kelimeler

• h-Kararlılık
• Mittag-Leffler kararlılık
• Kesirli fark denklemi
• Pertürbe denklem.

A note on the stability analysis of nonlinear fractional difference equations: Comparative approach

Abstract

In this study, we focus on nonlinear forward fractional difference equations with order ν∈(0,1] and construct stability analysis regarding h-stability and Mittag-Leffler stability notions. The main results of the paper are obtained by equiparating the equation in the spotlight with an auxiliary fractional difference equation. The outcomes of the manuscript provide an alternative approach to the ongoing theory of discrete fractional equations since the method used in the main results deviates from the fundamental tools of stability theory, namely fixed point theory and Liapunov's direct method.

Keywords

• h-stability
• Mittag-Leffler stability
• Forward fractional difference equation
• Perturbed equation.

Kaynakça

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