On Lyapunov stability of Caputo fractional dynamic equations on time scale using vector Lyapunov functions

Document Type : Original Article

Authors

Michael Precious Ineh ¹

Edet Peter Akpan ²

¹ Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Ritman University, Ikot Ekpene, Akwa Ibom State, Nigeria.

² Department of Mathematics, Faculty of Physical Sciences, Akwa-Ibom State University, Ikot Akpaden, Akwa Ibom State, Nigeria.

10.22034/kjm.2025.477875.3319

Abstract

This work extends the stability analysis of nonlinear fractional dynamic systems on time scales by introducing a new definition of the Caputo fractional delta derivative and Caputo delta Dini derivative for vector Lyapunov functions. The proposed framework effectively captures continuous and discrete dynamics,  making it well-suited for hybrid systems. Based on this new formulation for the Caputo fractional delta derivative of vector Lyapunov function, comparison results‎, ‎stability and asymptotic stability criteria for the investigated Caputo fractional dynamic equations are presented with practical examples demonstrating the applicability and effectiveness of our method‎.

Keywords

Stability

Caputo derivative

vector Lyapunov function

fractional dynamic equation

time scale

Subjects

• 34 Ordinary differential equations

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