Year: 2025
Type: article
Abstract: This paper investigates a car-following model that incorporates both classical and fractional discrete operators. While classical models have been extensively studied, the influence of discrete fractional operators on the stability of such systems has not yet been systematically analyzed. Stability conditions are derived and rigorously proven for systems employing three widely used fractional h-difference operators—Grünwald–Letnikov, Riemann–Liouville, and Caputo—as well as the classical h-difference operator. The analysis reveals that the established conditions are independent of the specific operator used. Furthermore, a comprehensive numerical study validates the theoretical findings and demonstrates that the fractional models can significantly extend the stability bound for the step size from h<6.67 (classical case) to h<22.3 (fractional case).
Source: Applied Sciences
DOI: 10.3390/app152011071
Authors: Katarzyna Topolewicz, Ewa Girejko
Institution: Bialystok University of Technology
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Funder: Politechnika Bialostocka
Award: G3751695286
OpenAlex ID: W4415238904