IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1814-d823774.html
   My bibliography  Save this article

New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

Author

Listed:
  • Omar Kahouli

    (Department of Electronics Engineering, Community College, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Assaad Jmal

    (Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia)

  • Omar Naifar

    (Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia)

  • Abdelhameed M. Nagy

    (Department of Mathematics, Faculty of Science, Kuwait University, Safat 13060, Kuwait
    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt)

  • Abdellatif Ben Makhlouf

    (Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72311, Saudi Arabia)

Abstract

In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced. This class is noteworthy to investigate, as it presents a generalization of the well-known Caputo fractional-order systems. In this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven. The Caputo–Katugampola fractional derivative concept, which involves two parameters 0 < α < 1 and ρ > 0, was used. Then, using the demonstrated barbalat-like lemma, two identification problems, namely, the “Fractional Error Model 1” and the “Fractional Error Model 1 with parameter constraints”, were studied and solved. Numerical simulations were carried out to validate our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1814-:d:823774
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1814/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1814/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    2. Pillai, Dhanup S. & Rajasekar, N., 2018. "Metaheuristic algorithms for PV parameter identification: A comprehensive review with an application to threshold setting for fault detection in PV systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 3503-3525.
    3. 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. Ying Zhang & Guifang Qiao & Qi Wan & Lei Tian & Di Liu, 2023. "A Novel Double-Layered Central Pattern Generator-Based Motion Controller for the Hexapod Robot," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    2. Fang Yan & Xiaorong Hou & Tingting Tian, 2022. "Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law," Mathematics, MDPI, vol. 10(18), pages 1-13, September.

    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. 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.
    2. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    3. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    4. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    5. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    6. 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.
    7. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    8. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    9. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    10. 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).
    11. Benjemaa, Mondher, 2018. "Taylor’s formula involving generalized fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 182-195.
    12. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    13. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    14. Schellenberg, C. & Lohan, J. & Dimache, L., 2020. "Comparison of metaheuristic optimisation methods for grid-edge technology that leverages heat pumps and thermal energy storage," Renewable and Sustainable Energy Reviews, Elsevier, vol. 131(C).
    15. Nawal Rai & Amel Abbadi & Fethia Hamidia & Nadia Douifi & Bdereddin Abdul Samad & Khalid Yahya, 2023. "Biogeography-Based Teaching Learning-Based Optimization Algorithm for Identifying One-Diode, Two-Diode and Three-Diode Models of Photovoltaic Cell and Module," Mathematics, MDPI, vol. 11(8), pages 1-30, April.
    16. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    17. 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).
    18. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    19. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.
    20. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(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:gam:jmathe:v:10:y:2022:i:11:p:1814-:d:823774. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.