IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2012y2012i1n417942.html

Numerical Solutions of a Variable‐Order Fractional Financial System

Author

Listed:
  • Shichang Ma
  • Yufeng Xu
  • Wei Yue

Abstract

The numerical solution of a variable‐order fractional financial system is calculated by using the Adams‐Bashforth‐Moulton method. The derivative is defined in the Caputo variable‐order fractional sense. Numerical examples show that the Adams‐Bashforth‐Moulton method can be applied to solve such variable‐order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable‐order fractional financial system with proper order functions.

Suggested Citation

  • Shichang Ma & Yufeng Xu & Wei Yue, 2012. "Numerical Solutions of a Variable‐Order Fractional Financial System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:417942
    DOI: 10.1155/2012/417942
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/417942
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/417942?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
    ---><---

    References listed on IDEAS

    as
    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    3. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    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. Lei He & Xiong Wang, 2014. "Parameters Estimation and Stability Analysis of Nonlinear Fractional‐Order Economic System Based on Empirical Data," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Yiding Yue & Lei He & Guanchun Liu, 2013. "Modeling and Application of a New Nonlinear Fractional Financial Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

    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. 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.
    2. 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.
    3. Lenka, Bichitra Kumar, 2025. "New stability theory for non-autonomous fractional time-varying order derivative systems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    4. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    5. Huang, Chengdai & Cao, Jinde, 2017. "Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 262-275.
    6. Ren, Jinfu & Liu, Yang & Liu, Jiming, 2023. "Chaotic behavior learning via information tracking," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. 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).
    8. Qu, Hai-Dong & Liu, Xuan & Lu, Xin & ur Rahman, Mati & She, Zi-Hang, 2022. "Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    9. 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.
    10. 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).
    11. 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).
    12. 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.
    13. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    14. 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 synchronization using optimized fractional order sli," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    15. 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).
    16. 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).
    17. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
    18. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    19. 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.
    20. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2012:y:2012:i:1:n:417942. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.