Stability of higher-order nonlinear impulsive differential equations

By Shuhong Tang, Akbar Zada, Shah Faisal, M. El-Sheikh, Tongxing Li. 2016

53 citations recorded by the source corpus.

For a higher-order nonlinear impulsive ordinary differential equation, we present the concepts of Hyers– Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers– Ulam–Rassias stability. Furthermore, we prove the generalized Hyers–Ulam–Rassias stability by using integral inequality of Grönwall type for piecewise continuous functions. These results extend related contributions to the corresponding first-order impulsive ordinary differential equation. Hyers–Ulam stability, generalized Hyers–Ulam stability, and Hyers–Ulam–Rassias stability can be discussed by the same methods. c ©2016 All rights reserved.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7e9639eea6f03aaefe4a2bc9dcf8ea37272819de

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In Applied Mathematics

1. Akbar Zada
2. Syed Omar Shah
3. Wajid Ali
4. S. Farina

In Control and Systems Engineering

1. S. Farina
2. Akbar Zada
3. Wajid Ali

In Numerical Analysis

1. Syed Omar Shah
2. Akbar Zada
3. Wajid Ali
4. S. Farina

Citations in the corpus

• Hyers–Ulam stability of nonlinear differential equations with fractional integrable impulses (2017, methodology): “Research in this paper is strongly motivated by the work presented in [34, 38].”
• Hyers-Ulam stability of first-order non-linear delay differential equations with fractional integrable impulses (2017, background): “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].”