IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v114y2018icp202-215.html
   My bibliography  Save this article

Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems

Author

Listed:
  • Mousavi, Yashar
  • Alfi, Alireza

Abstract

This paper deals with the parameters estimation problem of chaotic systems using firefly algorithm (FA). The main contribution of the present work is to introduce a modified version of FA by incorporating fractional calculus during the search process, namely fractional-order FA (FOFA). FOFA simulates the behavior of each firefly with more historical memory, leading to enhance the performance of the basic FA by controlling its convergence speed. A simple structure and straightforward to implement are the main aspects of the proposed FOFA. First, the capability of FOFA is evaluated on the well-known test functions adopted from CEC'2015. Then, FOFA is applied for parameter estimation of chaotic systems. Results reveal that the incorporation of a memory term into the FA is an extremely significant development in comparison with other types of FAs.

Suggested Citation

  • Mousavi, Yashar & Alfi, Alireza, 2018. "Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 202-215.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:202-215
    DOI: 10.1016/j.chaos.2018.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791830537X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.07.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    2. Yu, Shuhao & Zhu, Shenglong & Ma, Yan & Mao, Demei, 2015. "A variable step size firefly algorithm for numerical optimization," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 214-220.
    3. Alfi, Alireza, 2012. "Chaos suppression on a class of uncertain nonlinear chaotic systems using an optimal H∞ adaptive PID controller," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 351-357.
    4. Ahmadi, Mohamadreza & Mojallali, Hamed, 2012. "Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1108-1120.
    5. Turalska, Malgorzata & West, Bruce J., 2017. "A search for a spectral technique to solve nonlinear fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 387-395.
    6. Li, Chaoshun & Zhou, Jianzhong & Xiao, Jian & Xiao, Han, 2012. "Parameters identification of chaotic system by chaotic gravitational search algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 539-547.
    7. Banerjee, Amit & Abu-Mahfouz, Issam, 2014. "A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 65-83.
    8. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Bin & Ren, Yi & Gao, Diankui & Xu, Lizhi, 2019. "Performance ratio prediction of photovoltaic pumping system based on grey clustering and second curvelet neural network," Energy, Elsevier, vol. 171(C), pages 360-371.
    2. Abedi Pahnehkolaei, Seyed Mehdi & Alfi, Alireza & Tenreiro Machado, J.A., 2022. "Analytical stability analysis of the fractional-order particle swarm optimization algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Mehmood, Ammara & Raja, Muhammad Asif Zahoor & Jalili, Mahdi, 2023. "Optimization of integrated load dispatch in multi-fueled renewable rich power systems using fractal firefly algorithm," Energy, Elsevier, vol. 278(PA).
    4. Chou, Jui-Sheng & Truong, Dinh-Nhat, 2020. "Multiobjective optimization inspired by behavior of jellyfish for solving structural design problems," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    5. Yashar Mousavi & Geraint Bevan & Ibrahim Beklan Küçükdemiral & Afef Fekih, 2021. "Maximum Power Extraction from Wind Turbines Using a Fault-Tolerant Fractional-Order Nonsingular Terminal Sliding Mode Controller," Energies, MDPI, vol. 14(18), pages 1-16, September.
    6. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. Mousavi, Yashar & Bevan, Geraint & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Sliding mode control of wind energy conversion systems: Trends and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 167(C).
    8. Cui, Yibing & Hu, Wei & Rahmani, Ahmed, 2023. "Fractional-order artificial bee colony algorithm with application in robot path planning," European Journal of Operational Research, Elsevier, vol. 306(1), pages 47-64.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Verma, S. & Viswanathan, P., 2018. "A note on Katugampola fractional calculus and fractal dimensions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 220-230.
    2. Benjemaa, Mondher, 2018. "Taylor’s formula involving generalized fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 182-195.
    3. Yang, Zhanwen & Li, Qi & Yao, Zichen, 2023. "A stability analysis for multi-term fractional delay differential equations with higher order," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Izadi, Mohammad & Srivastava, H.M., 2021. "Numerical approximations to the nonlinear fractional-order Logistic population model with fractional-order Bessel and Legendre bases," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Sarita Kumari & Rajesh K. Pandey & Ravi P. Agarwal, 2023. "High-Order Approximation to Generalized Caputo Derivatives and Generalized Fractional Advection–Diffusion Equations," Mathematics, MDPI, vol. 11(5), pages 1-24, February.
    6. Ren, Jing & Zhai, Chengbo, 2020. "Stability analysis for generalized fractional differential systems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
    9. Faten Fakher Abdulnabi & Hiba F. Al-Janaby & Firas Ghanim & Alina Alb Lupaș, 2023. "Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    10. Omar Kahouli & Assaad Jmal & Omar Naifar & Abdelhameed M. Nagy & Abdellatif Ben Makhlouf, 2022. "New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    11. Banerjee, Amit & Abu-Mahfouz, Issam, 2014. "A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 65-83.
    12. Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D.G. & Gao, Wei & Yel, Gulnur, 2020. "Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    13. Bezruchko, B.P. & Ponomarenko, V.I. & Smirnov, D.A. & Sysoev, I.V. & Prokhorov, M.D., 2021. "Class-oriented techniques for reconstruction of dynamics from time series," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    14. Chunyuan Zhang & Pengyu Chen & Fangling Jiang & Jinsen Xie & Tao Yu, 2023. "Fault Diagnosis of Nuclear Power Plant Based on Sparrow Search Algorithm Optimized CNN-LSTM Neural Network," Energies, MDPI, vol. 16(6), pages 1-17, March.
    15. Abdelfattah Mustafa & Reda S. Salama & Mokhtar Mohamed, 2023. "Analysis of Generalized Nonlinear Quadrature for Novel Fractional-Order Chaotic Systems Using Sinc Shape Function," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    16. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Syam, Muhammed I. & Sharadga, Mwaffag & Hashim, I., 2021. "A numerical method for solving fractional delay differential equations based on the operational matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. B. Koti Reddy & Amit Kumar Singh, 2021. "Optimal Operation of a Photovoltaic Integrated Captive Cogeneration Plant with a Utility Grid Using Optimization and Machine Learning Prediction Methods," Energies, MDPI, vol. 14(16), pages 1-28, August.
    19. Pundikala Veeresha & Doddabhadrappla Gowda Prakasha & Dumitru Baleanu, 2019. "An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    20. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:202-215. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.