IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics0960077921000011.html
   My bibliography  Save this article

Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay

Author

Listed:
  • Kumar, Surendra
  • Sharma, Abhishek
  • Pal Singh, Harendra

Abstract

In this paper, a new numerical scheme termed as fractional delay block boundary value methods (FDBBVMs) is proposed. It is an extended version of the block boundary value methods (BBVMs). The proposed scheme is used to find numerical solutions of the fractional delay differential equations including Caputo fractional derivative of βth order with 0<β<1 and a constant delay term. The estimation of the fractional-order derivative term is obtained by combining the mth-order Lagrange interpolating polynomial along with the pth-order BBVMs, and the constant delay term is dealt with certain modifications in the BBVM. Further, the convergence analysis of the proposed scheme is discussed and it is observed that the FDBBVM is convergent with order min{p,m−β+1}. Moreover, the scheme is shown to be globally stable and its computational efficiency and accuracy has been illustrated with the help of numerical examples.

Suggested Citation

  • Kumar, Surendra & Sharma, Abhishek & Pal Singh, Harendra, 2021. "Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000011
    DOI: 10.1016/j.chaos.2021.110648
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921000011
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110648?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. Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
    2. Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
    3. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    4. Yan, Xiaoqiang & Zhang, Chengjian, 2019. "Solving nonlinear functional–differential and functional equations with constant delay via block boundary value methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 21-32.
    5. Zhang, Chengjian & Chen, Hao, 2010. "Asymptotic stability of block boundary value methods for delay differential-algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 100-108.
    Full references (including those not matched with items on IDEAS)

    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. Ren, Jinfu & Liu, Yang & Liu, Jiming, 2023. "Chaotic behavior learning via information tracking," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. 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.
    4. Fendzi Donfack, Emmanuel & Nguenang, Jean Pierre & Nana, Laurent, 2020. "On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    6. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    7. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    8. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    9. 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).
    10. Yu, Qiang & Turner, Ian & Liu, Fawang & Vegh, Viktor, 2022. "The application of the distributed-order time fractional Bloch model to magnetic resonance imaging," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    11. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    12. Runzi Luo & Haipeng Su, 2018. "The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output," Complexity, Hindawi, vol. 2018, pages 1-8, November.
    13. Xu, Fei & Lai, Yongzeng & Shu, Xiao-Bao, 2018. "Chaos in integer order and fractional order financial systems and their synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 125-136.
    14. Chenhui Wang, 2016. "Adaptive Fuzzy Control for Uncertain Fractional-Order Financial Chaotic Systems Subjected to Input Saturation," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-17, October.
    15. Huang, Conggui & Wang, Fei & Zheng, Zhaowen, 2021. "Exponential stability for nonlinear fractional order sampled-data control systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    16. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
    17. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    18. Lin, Zifei & Li, Jiaorui & Li, Shuang, 2016. "On a business cycle model with fractional derivative under narrow-band random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 61-70.
    19. Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    20. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.

    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:144:y:2021:i:c:s0960077921000011. 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.