Year: 2026
Type: article
Abstract: This paper investigates a friction oscillator model in both its Integer-Order and Fractional-Order formulations. The lack of classical solutions for the governing differential equations with discontinuous right-hand sides is addressed by adopting a Differential Inclusion framework. Using Filippov regularization, the discontinuity is replaced by a set-valued map satisfying appropriate regularity conditions. Selection theory is then applied to construct a Lipschitz-continuous, single-valued function that approximates the set-valued map. This procedure reformulates the discontinuous initial value problem as a continuous, single-valued one, thereby providing a rigorous justification for the proposed approximation method. Numerical simulations are performed to study stick–slip attractors in both the Integer-Order and Fractional-Order cases. The results demonstrate that, in contrast to the Integer-Order system, periodic attractors cannot occur in the Fractional-Order regime.
Source: Fractal and Fractional
Author: Marius-F. Danca
Institution: Babeș-Bolyai University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W7118459496