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Study on fractional order gradient methods

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  • Chen, Yuquan
  • Gao, Qing
  • Wei, Yiheng
  • Wang, Yong

Abstract

In this paper, convergence capability of the conventional fractional order gradient methods (FOGMs) is analyzed and a new FOGM with guaranteed and faster convergence ability is proposed. In particular, we further consider the case that the derivative order varies between 1 and 2, and give some discussion on how to determine the derivative order in the algorithm settings. Simulation results from a number of numerical examples are provided to illustrate the approaches.

Suggested Citation

  • Chen, Yuquan & Gao, Qing & Wei, Yiheng & Wang, Yong, 2017. "Study on fractional order gradient methods," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 310-321.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:310-321
    DOI: 10.1016/j.amc.2017.07.023
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    References listed on IDEAS

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    1. Zhang, Xuxi & Liu, Xianping & Zhu, Qidan, 2014. "Adaptive chatter free sliding mode control for a class of uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 431-435.
    2. Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
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    Cited by:

    1. Zijian Liu & Yaning Wang & Yang Luo & Chunbo Luo, 2022. "A Regularized Graph Neural Network Based on Approximate Fractional Order Gradients," Mathematics, MDPI, vol. 10(8), pages 1-20, April.
    2. Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Zeshan Aslam Khan & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle," Mathematics, MDPI, vol. 9(24), pages 1-14, December.
    3. Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Liu, Jianjun & Zhai, Rui & Liu, Yuhan & Li, Wenliang & Wang, Bingzhe & Huang, Liyuan, 2021. "A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    5. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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