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Fractal derivative fractional grey Riccati model and its application

Author

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  • Zhang, Yonghong
  • Mao, Shuhua
  • Kang, Yuxiao
  • Wen, Jianghui

Abstract

Fractal geometry methods are widely used to describe the geometric characteristics of complex systems, statistical behaviors, and power-law characteristics of data results. In this study, the fractal derivative and fractional cumulative generating operators are introduced into the grey Riccati model to establish the fractal derivative and fractional grey Riccati model (FDFGRM), and the analytical solution of the model is obtained. At the same time, multi-objective quantum particle swarm optimization algorithm is used for parameter optimization. We consider China's cement production, natural gas production, and primary aluminum production as examples to verify the validity of the model. The results show that the fitting and testing effects of the FDFGRM are better than those of other models. Finally, FDFGRM is used to predict the future trends of these three cases.

Suggested Citation

  • Zhang, Yonghong & Mao, Shuhua & Kang, Yuxiao & Wen, Jianghui, 2021. "Fractal derivative fractional grey Riccati model and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001302
    DOI: 10.1016/j.chaos.2021.110778
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Wang, Yong & Yang, Zhongsen & Wang, Li & Ma, Xin & Wu, Wenqing & Ye, Lingling & Zhou, Ying & Luo, Yongxian, 2022. "Forecasting China's energy production and consumption based on a novel structural adaptive Caputo fractional grey prediction model," Energy, Elsevier, vol. 259(C).
    2. Kang, Yuxiao & Mao, Shuhua & Zhang, Yonghong, 2022. "Fractional time-varying grey traffic flow model based on viscoelastic fluid and its application," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 149-174.
    3. Zhenguo Xu & Wanli Xie & Caixia Liu, 2023. "An Optimized Fractional Nonlinear Grey System Model and Its Application in the Prediction of the Development Scale of Junior Secondary Schools in China," Sustainability, MDPI, vol. 15(4), pages 1-12, February.
    4. Zhang, Yonghong & Li, Shouwei & Li, Jingwei & Tang, Xiaoyu, 2022. "A time power-based grey model with Caputo fractional derivative and its application to the prediction of renewable energy consumption," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. He, Jing & Mao, Shuhua & Kang, Yuxiao, 2023. "Augmented fractional accumulation grey model and its application: Class ratio and restore error perspectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 220-247.

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