IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v251y2015icp475-488.html
   My bibliography  Save this article

Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis

Author

Listed:
  • Chen, Yiming
  • Ke, Xiaohong
  • Wei, Yanqiao

Abstract

In this paper, a system of nonlinear fractional differential equations (FDEs) are considered. They have been solved by Legendre wavelets method combining with its operational matrix. However, there are no articles about solving this system using wavelets method. The main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily. The convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem. Finally, the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples.

Suggested Citation

  • Chen, Yiming & Ke, Xiaohong & Wei, Yanqiao, 2015. "Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 475-488.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:475-488
    DOI: 10.1016/j.amc.2014.11.079
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314016117
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.11.079?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. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
    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, Fuqiang & Huang, Qingxue & Xie, Jiaquan & Li, Yugui & Ma, Lifeng & Wang, Jianmei, 2017. "Chebyshev polynomials approach for numerically solving system of two-dimensional fractional PDEs and convergence analysis," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 321-330.
    2. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.
    3. Doungmo Goufo, Emile F. & Khan, Yasir & Chaudhry, Qasim Ali, 2020. "HIV and shifting epicenters for COVID-19, an alert for some countries," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Rehman, Mujeeb ur & Idrees, Amna & Saeed, Umer, 2017. "A quadrature method for numerical solutions of fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 38-49.
    5. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    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. Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    2. 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.
    3. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    4. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    5. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    6. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    8. Muñoz-Vázquez, Aldo Jonathan & Ortiz-Moctezuma, Manuel Benjamín & Sánchez-Orta, Anand & Parra-Vega, Vicente, 2019. "Adaptive robust control of fractional-order systems with matched and mismatched disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 85-96.
    9. Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    10. Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    11. Zhu, Hao & Zhou, Shangbo & Zhang, Jun, 2009. "Chaos and synchronization of the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1595-1603.
    12. Naik, Manisha Krishna & Baishya, Chandrali & Veeresha, P., 2023. "A chaos control strategy for the fractional 3D Lotka–Volterra like attractor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 1-22.
    13. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    14. Dongya Li & Xiaoping Zhang & Shuang Wang & Fengxiang You, 2022. "Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    15. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2018. "Applications of Lyapunov Functions to Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    16. Huang, Xiuqi & Wang, Xiangjun, 2021. "Regularity of fractional stochastic convolution and its application to fractional stochastic chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    17. Zhang, Zhe & Zhang, Jing & Ai, Zhaoyang & Cheng, FanYong & Liu, Feng, 2020. "A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 328-344.
    18. Zhang, Chaoxia & Yu, Simin, 2011. "Generation of multi-wing chaotic attractor in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 845-850.
    19. Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
    20. Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.

    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:apmaco:v:251:y:2015:i:c:p:475-488. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.