Halanay type inequalities on time scales with applications
Murat Ad{\i}var, Elvan Ak{\i}n Bohner
TL;DR
This paper introduces Halanay type inequalities on time scales, providing new stability criteria for nonlinear dynamic equations and extending existing theories to more general cases including q-difference equations.
Contribution
It generalizes Halanay inequalities to time scales, offering improved stability conditions and extending results to q-difference cases.
Findings
New global stability conditions for nonlinear dynamic equations.
Extensions to q-difference equations.
Improvements over existing differential and difference inequalities.
Abstract
This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that beside generalization and extension to q-difference case, our results also provide improvements for the existing theory regarding differential and difference inequalites, which are the most important particular cases of dynamic inequalities on time scales.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Fractional Differential Equations Solutions · Stability and Controllability of Differential Equations