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Peer-reviewedCC BY 4.0Fractal and Fractional

Equation-Free Screening of Mittag–Leffler Compatibility from Multi-Horizon Relaxation Profiles

  • N’Gbo N’Gbo1,2
  • Andrei Velichko3
  • Bruno Carpentieri4
4 affiliations
  1. 1School of Science and Engineering, International University of Grand-Bassam, Route de Bonoua, Grand-Bassam BP 564, Côte d’Ivoire
  2. 2Laboratory for Intelligence and Mathematics (LIMAs), Route de Bonoua, Grand-Bassam BP 564, Côte d’Ivoire
  3. 3Institute of Physics and Technology, Petrozavodsk State University, 33 Lenina Prospekt, Petrozavodsk 185910, Republic of Karelia, Russia
  4. 4Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi 1, 39100 Bozen–Bolzano, Italy
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Abstract

We study an equation-free screen for finite-window Mittag–Leffler compatibility, in which multi-horizon relaxation profiles are constructed out of sample by k-nearest-neighbor prediction from ensembles of scalar trajectories and compared with candidate temporal laws. The screen assesses compatibility, not the generating mechanism. In a matched, noise-free calibration, it reproduces the generating Mittag–Leffler behavior to numerical precision, while relaxation-rate heterogeneity shifts the fitted Mittag–Leffler order toward lower values. For noise-free classical distributed-rate ensembles, a Mittag–Leffler preference over a single exponential disappears when a biexponential alternative is included. Under observational noise, this recovery is incomplete: with three candidate families, the Mittag–Leffler law is still selected in 60% of runs for a classical ensemble, against 72% for a fractional reference. In the tested noise-free settings, simpler profile constructions reproduce the screening decisions, whereas kNN predicts individual trajectories far more accurately than a constant predictor. The screening interpretation of a single-record example, initially investigated as a chaotic test case, is withdrawn as evidence about the continuous system after numerical verification revealed a nonrobust simulated regime. Mittag–Leffler compatibility is therefore a comparative, condition-dependent screening outcome, not identification of fractional origin.

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Cite

BibTeXRIS
BibTeX
@article{ngbo2026equationfree,
  title = {{Equation-Free Screening of Mittag–Leffler Compatibility from Multi-Horizon Relaxation Profiles}},
  author = {N’Gbo N’Gbo and Andrei Velichko and Bruno Carpentieri},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10110745},
  url = {https://www.mdpi.com/2504-3110/10/11/745},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Equation-Free Screening of Mittag–Leffler Compatibility from Multi-Horizon Relaxation Profiles
AU  - N’Gbo N’Gbo
AU  - Andrei Velichko
AU  - Bruno Carpentieri
PY  - 2026
DA  - 2026/10/26
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10110745
UR  - https://www.mdpi.com/2504-3110/10/11/745
AB  - We study an equation-free screen for finite-window Mittag–Leffler compatibility, in which multi-horizon relaxation profiles are constructed out of sample by k-nearest-neighbor prediction from ensembles of scalar trajectories and compared with candidate temporal laws. The screen assesses compatibility, not the generating mechanism. In a matched, noise-free calibration, it reproduces the generating Mittag–Leffler behavior to numerical precision, while relaxation-rate heterogeneity shifts the fitted Mittag–Leffler order toward lower values. For noise-free classical distributed-rate ensembles, a Mittag–Leffler preference over a single exponential disappears when a biexponential alternative is included. Under observational noise, this recovery is incomplete: with three candidate families, the Mittag–Leffler law is still selected in 60% of runs for a classical ensemble, against 72% for a fractional reference. In the tested noise-free settings, simpler profile constructions reproduce the screening decisions, whereas kNN predicts individual trajectories far more accurately than a constant predictor. The screening interpretation of a single-record example, initially investigated as a chaotic test case, is withdrawn as evidence about the continuous system after numerical verification revealed a nonrobust simulated regime. Mittag–Leffler compatibility is therefore a comparative, condition-dependent screening outcome, not identification of fractional origin.
SN  - 2504-3110
ER  -