On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations

By Akbar Zada, Shah Faisal, Yongjin Li. 2016

63 citations recorded by the source corpus.

This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval. Our approach uses abstract Gronwall lemma together with integral inequality of Gronwall type for piecewise continuous functions.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ff6cdadb6194e2893e2c85774284e86477163639

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Akbar Zada
2. Syed Omar Shah
3. Tongxing Li
4. Shah Faisal

In Numerical Analysis

1. Akbar Zada
2. Syed Omar Shah
3. Tongxing Li

Citations in the corpus

• Hyers-Ulam stability of first-order non-linear delay differential equations with fractional integrable impulses (2017, methodology): “For more details on Hyers Ulam stability, we recommend [3, 6, 7, 8, 9, 11, 13, 14, 15, 16, 19, 24, 26, 30, 34, 36, 37, 38, 39, 40, 41, 42, 29].”
• Stability of higher-order nonlinear impulsive differential equations (2016, background): “In recent years, Hyers–Ulam stability and Hyers–Ulam–Rassias stability of impulsive differential equations have always attracted interest of researchers; see, for instance, [3, 14, 19, 26, 27, 33].”