Work

A robust uniform practical stability approach for Caputo fractional hybrid systems

Year: 2025

Type: article

Abstract: This work introduces a novel approach for analyzing the uniform practical stability (UPS) and strong uniform practical stability (SUPS) of Caputo fractional dynamic equations on time scales, using two measures ($ m, m_0 $). The method employs an extended derivative, the Caputo fractional delta Dini derivative (CFr$ \Delta $DiD) of order $\zeta \in (0, 1)$, addressing the gap in unified stability frameworks for fractional hybrid systems that span both continuous and discrete time domains. This generalized framework not only unifies various stability concepts but also makes it applicable to hybrid systems with both gradual and abrupt changes. The UPS and SUPS results are demonstrated through illustrative examples.

Source: AIMS Mathematics

DOI: 10.3934/math.2025320

Authors: Michael Precious Ineh, Umar Ishtiaq, Jackson Efiong Ante, Mubariz Garayev, Ioan-Lucian Popa

Institutions: University of Management and Technology, Topfaith University, King Saud University, Transylvania University of Brașov, 1 Decembrie 1918 University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: King Saud University