On the Auxiliary Lyapunov Functions and Uniform Practical Stability for Nonlinear Impulsive Caputo Fractional Order Derivative via New Modelled Generalized Dini Derivative

Authors

  • J. U., Atsu Department of Mathematics, University of Cross River State, Calabar
  • J. E. Ante Department of Mathematics, Topfaith University, Mkpatak, Nigeria 3Department of Statistics, Federal Polytechnic, Ugep
  • R. E Francis Department of Statistics, Federal Polytechnic, Ugep
  • S. O. Essang Department of Mathematics, Arthur Jarvis University, Akpabuyo, Calabar
  • R. D. Effiong Department of Mathematics, University of Calabar, Calabar
  • Jonathan Timothy Auta Department of Pure/Applied Mathematics, African University of Science and Technology, Abuja

Keywords:

Uniform practical stability, Caputo derivative, impulse, Lyapunov function

Abstract

In this paper, the uniform practical stability of the trivial solution of a nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse is examined using an  auxilliary Lyapunov function which are analogues of vector Lyapunov functions, and is  generalized by a class of piecewise continuous Lyapunov functions. Together with comparison  results, sufficient conditions for the uniform practical stability for impulsive Caputo fractional  order systems are established. An illustrative example is given to confirm the suitability of the obtained results.

Additional Files

Published

2025-02-16

How to Cite

Atsu, J. U., Ante, J. E., Francis, R. E., Essang, S. O., Effiong, R. D., & Auta, . J. . T. (2025). On the Auxiliary Lyapunov Functions and Uniform Practical Stability for Nonlinear Impulsive Caputo Fractional Order Derivative via New Modelled Generalized Dini Derivative. Journal of Science Education and Humanities, 8(1). Retrieved from https://akscoejoseh.org.ng/index.php/joseh/article/view/13

Issue

Vol. 8 No. 1 (2024): Volume 8, Issue 1, 2024

Section

Articles