A NOTE ON THE INCOMPATIBILITY OF AUTONOMOUS FRACTIONAL DIFFERENTIAL SYSTEMS AND FRACTIONAL DERIVATIVES WITH NON-SINGULAR KERNELS
This paper addresses a critical oversight in the modeling of autonomous fractional differential systems using fractional derivatives with non-singular kernels such as the Caputo–Fabrizio (CF) and Atangana–Baleanu–Caputo (ABC) derivatives. We demonstrate that for such systems to be well defined, the initial condition must be an equilibrium point, which significantly limits the practical applicability of these models, a fact often overlooked in existing studies, leading to incorrect conclusions.
Authors
- Nabil Barhoumi (ORCID: https://orcid.org/0009-0002-9082-5307)
- Redouane Douaifia (ORCID: https://orcid.org/0000-0001-6960-4572)
- Samir Bendoukha (ORCID: https://orcid.org/0000-0002-1171-7854)
- Mathkar A. Alharthi (ORCID: https://orcid.org/0000-0002-2562-670X)
- Emad M. Ali (ORCID: https://orcid.org/0000-0003-0657-2379)
- Salem Abdelmalek
Institutions
- Yanbu University College (SA)
- University of Monastir (TN)
- King Saud University (SA)
- Université Larbi Tébessi (DZ)
- University of Blida (DZ)
Publication Details
- Journal
- Fractals
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1142/s0218348x25401644
- Citations
- 1
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 1.37