A Lyapunov-based approach to uniform strict stability analysis for nonlinear impulsive Caputo fractional derivatives with weakly singular kernel

##article.authors##

  • J.U. Atsu Department of Mathematics, University of Cross Rivers State, Calabar, Nigeria;
  • J.E. Ante Department of Mathematics, Topfaith University, Mkpatak, Akwa Ibom State, Nigeria
  • C.M. Orazulume Department of Electrical/Electronics, Topfaith University, Mkpatak, Nigeria
  • S.O. Essang Department of Mathematics and Computer Science, Arthur Jarvis University, Akpabuyo, Cross River State, Nigeria;
  • R.E. Francis Department of Statistics, Federal Polytechnic, Ugep, Nigeria
  • S.I. Okeke Department of Industrial Mathematics and Health Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria.
  • W.K. Udogworen Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Mkpat-Enin.

##semicolon##

uniform strict stability, Caputo derivative, impulse, vector Lyapunov function, fractional differential equation.

##article.abstract##

This study explores the uniform strict stability of nonlinear impulsive Caputo fractional differential equations (ICFrDEs) by utilizing a powerful framework of vector Lyapunov functions which is generalized by a class of piecewise continuous Lyapunov functions. By integrating comparison results and employing this new class of Lyapunov functions, comprehensive sufficient conditions for uniform strict stability are derived. The applicability and significance of these findings are illustrated through a detailed example, which demonstrates the improvements over existing results and highlights the broader implications of this approach. This research contributes significantly to the analysis of uniform strict stability of ICFrDEs, providing a robust framework for future studies.

##submission.downloads##

##submissions.published##

2025-07-23

##submission.howToCite##

Atsu, J. ., Ante, J., Orazulume, C. ., Essang, . S. ., Francis, R., Okeke, S. ., & Udogworen, W. . (2025). A Lyapunov-based approach to uniform strict stability analysis for nonlinear impulsive Caputo fractional derivatives with weakly singular kernel. International Journal of Mathematical Analysis and Modelling, 8(1). Retrieved from https://tnsmb.org/journal/index.php/ijmam/article/view/221

##issue.issue##

##issue.vol## 8 ##issue.no## 1 (2025): Volume 8, No. 1, 2025

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