Practical stability of Caputo fractional dynamic equations on time scale

Abstract

This paper presents a novel approach to analyzing the practical stability of Caputo fractional dynamic equations on time scales, utilizing a new generalized derivative known as the Caputo fractional delta derivative and the Caputo fractional delta Dini derivative of order α∈(0,1). This generalized derivative provides a unified framework for analyzing dynamic systems across both continuous and discrete time domains, making it suitable for hybrid systems exhibiting both gradual and abrupt changes. By incorporating memory effects inherent in fractional-order systems, this derivative is particularly suited to practical stability analysis, where deviations from equilibrium are permitted within acceptable limits. The established practical stability results are demonstrated through an illustrative example.