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Peer-reviewedCC BY 4.0Fractal and Fractional

Bicontrolled Contractive Approach to the Existence of Solutions to the Fractional Aizawa Model

  • Guimin Zhuang1
  • Jinqiu Guan1
  • Tahir Javed2
  • Muhammad Nazam2
  1. 1School of Science, Jiamusi University, Jiamusi 154007, China
  2. 2Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan
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Abstract

We introduce a novel class of (F,B)-contractions on complete metric spaces by imposing appropriate conditions on the auxiliary functions F and B. A new fixed-point theorem has been established, guaranteeing both the existence and uniqueness of the fixed point. This result brings together and expands upon several traditional contributions in fixed-point theory. The practicality of this theoretical framework is demonstrated through illustrative examples, including the existence and uniqueness of solutions to the fractional-order Aizawa system formulated with the Atangana–Baleanu fractional derivative. Numerical simulations, supported by graphical analysis and Lyapunov exponents, are presented to characterize the system’s dynamical behavior and to validate the effectiveness of the proposed results.

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Cite

BibTeXRIS
BibTeX
@article{zhuang2026bicontrolled,
  title = {{Bicontrolled Contractive Approach to the Existence of Solutions to the Fractional Aizawa Model}},
  author = {Guimin Zhuang and Jinqiu Guan and Tahir Javed and Muhammad Nazam},
  journal = {Fractal and Fractional},
  year = {2026},
  month = oct,
  doi = {10.3390/fractalfract10100688},
  url = {https://www.mdpi.com/2504-3110/10/10/688},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Bicontrolled Contractive Approach to the Existence of Solutions to the Fractional Aizawa Model
AU  - Guimin Zhuang
AU  - Jinqiu Guan
AU  - Tahir Javed
AU  - Muhammad Nazam
PY  - 2026
DA  - 2026/10/01
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10100688
UR  - https://www.mdpi.com/2504-3110/10/10/688
AB  - We introduce a novel class of (F,B)-contractions on complete metric spaces by imposing appropriate conditions on the auxiliary functions F and B. A new fixed-point theorem has been established, guaranteeing both the existence and uniqueness of the fixed point. This result brings together and expands upon several traditional contributions in fixed-point theory. The practicality of this theoretical framework is demonstrated through illustrative examples, including the existence and uniqueness of solutions to the fractional-order Aizawa system formulated with the Atangana–Baleanu fractional derivative. Numerical simulations, supported by graphical analysis and Lyapunov exponents, are presented to characterize the system’s dynamical behavior and to validate the effectiveness of the proposed results.
SN  - 2504-3110
ER  -