Stability analysis of Caputo fractional time-dependent systems with delay using vector lyapunov functions

Jonas Ogar Achuobi; Edet Peter Akpan; Reny George; Austine Efut Ofem; Jonas Ogar Achuobi; Edet Peter Akpan; Reny George; Austine Efut Ofem

doi:10.3934/math.20241362

AIMS Mathematics

2024, Volume 9, Issue 10: 28079-28099. doi: 10.3934/math.20241362

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Research article

Stability analysis of Caputo fractional time-dependent systems with delay using vector lyapunov functions

1.
Department of Mathematics, Akwa-Ibom State University, Ikot Akpaden, Akwa Ibom State, Nigeria
2.
Department of Mathematics, University of Calabar, Calabar, Nigeria
3.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharaj 11942, Saudi Arabia
4.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Received: 23 July 2024 Revised: 11 September 2024 Accepted: 20 September 2024 Published: 27 September 2024
MSC : 34A08, 34A34, 34D20, 34K37

In this study, we investigate the stability and asymptotic stability properties of Caputo fractional time-dependent systems with delay by employing vector Lyapunov functions. Utilizing the Caputo fractional Dini derivative on Lyapunov-like functions, along with a new comparison theorem and differential inequalities, we derive and prove sufficient conditions for the stability and asymptotic stability of these complex systems. An example is included to showcase the method's practicality and to specifically illustrate its advantages over scalar Lyapunov functions. Our results improves, extends, and generalizes several existing findings in the literature.
- stability,
- asymptotic stability,
- Caputo derivative,
- vector Lyapunov function,
- fractional delay differential equation
Citation: Jonas Ogar Achuobi, Edet Peter Akpan, Reny George, Austine Efut Ofem. Stability analysis of Caputo fractional time-dependent systems with delay using vector lyapunov functions[J]. AIMS Mathematics, 2024, 9(10): 28079-28099. doi: 10.3934/math.20241362

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Abstract

In this study, we investigate the stability and asymptotic stability properties of Caputo fractional time-dependent systems with delay by employing vector Lyapunov functions. Utilizing the Caputo fractional Dini derivative on Lyapunov-like functions, along with a new comparison theorem and differential inequalities, we derive and prove sufficient conditions for the stability and asymptotic stability of these complex systems. An example is included to showcase the method's practicality and to specifically illustrate its advantages over scalar Lyapunov functions. Our results improves, extends, and generalizes several existing findings in the literature.

References

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