Analyzing the fractional Chen attractor via controlled interpolative metric contractions

Ekber Girgin; Sertaç Erman; Abdurrahman Büyükkaya; Mahpeyker Öztürk; Ekber Girgin; Sertaç Erman; Abdurrahman Büyükkaya; Mahpeyker Öztürk

doi:10.3934/math.2026224

AIMS Mathematics

2026, Volume 11, Issue 3: 5436-5455. doi: 10.3934/math.2026224

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Analyzing the fractional Chen attractor via controlled interpolative metric contractions

1.
Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, 54050, Sakarya, Türkiye
2.
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Türkiye
3.
Department of Mathematics, Faculty of Sciences, Sakarya University, 54050, Sakarya, Türkiye
4.
Picode Software, Education Training Consultancy Research and Development and Trade Co., Ltd., 54050, Sakarya, Türkiye

Received: 16 November 2025 Revised: 15 February 2026 Accepted: 25 February 2026 Published: 03 March 2026
MSC : 47H10, 54H25

The present study advances the idea of controlled $ (\alpha, c) $–interpolative metric spaces as a broader framework that extends interpolative and extended interpolative frameworks and examines their analytical properties in conjunction with Banach-type fixed-point results. The proposed metric structure is then employed to study the fractional-order Chen attractor model defined via the Atangana–Baleanu–Caputo ($ \mathcal{ABC} $) derivative. Using the newly established metric framework, a suitable fixed-point operator is constructed in the Banach space $ C([0, T]; \mathbb{R}^3) $, and sufficient contraction conditions ensuring the existence and uniqueness of solutions are derived. The consistency and accuracy of the proposed numerical formulation are demonstrated through simulation results, highlighting improved sensitivity and richer chaotic behavior compared to integer-order models. The obtained results confirm that the controlled interpolative metric approach provides a flexible analytical tool for exploring nonlinear fractional systems and offers new insights into the stability analysis of chaotic dynamical models such as the Chen attractor.
- controlled metric space,
- interpolative metric space,
- fractional-order Chen attractor,
- chaotic dynamical models,
- nonlinear fractional systems
Citation: Ekber Girgin, Sertaç Erman, Abdurrahman Büyükkaya, Mahpeyker Öztürk. Analyzing the fractional Chen attractor via controlled interpolative metric contractions[J]. AIMS Mathematics, 2026, 11(3): 5436-5455. doi: 10.3934/math.2026224

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Abstract

The present study advances the idea of controlled $ (\alpha, c) $–interpolative metric spaces as a broader framework that extends interpolative and extended interpolative frameworks and examines their analytical properties in conjunction with Banach-type fixed-point results. The proposed metric structure is then employed to study the fractional-order Chen attractor model defined via the Atangana–Baleanu–Caputo ($ \mathcal{ABC} $) derivative. Using the newly established metric framework, a suitable fixed-point operator is constructed in the Banach space $ C([0, T]; \mathbb{R}^3) $, and sufficient contraction conditions ensuring the existence and uniqueness of solutions are derived. The consistency and accuracy of the proposed numerical formulation are demonstrated through simulation results, highlighting improved sensitivity and richer chaotic behavior compared to integer-order models. The obtained results confirm that the controlled interpolative metric approach provides a flexible analytical tool for exploring nonlinear fractional systems and offers new insights into the stability analysis of chaotic dynamical models such as the Chen attractor.

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