IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v98y2017icp44-45.html

Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method

Author

Listed:
  • Kavyanpoor, Mobin
  • Shokrollahi, Saeed

Abstract

In this letter, a solution of the fractional Van Der Pol equation that uses the differential transform method has been investigated. In previous studies this method was incorrectly applied to the fractional Van Der Pol oscillator and inaccurate results were obtained. In this note, true solution of the problem has been presented. Although it was shown that, this method is not appropriate and a non-periodic solution was obtained.

Suggested Citation

  • Kavyanpoor, Mobin & Shokrollahi, Saeed, 2017. "Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 44-45.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:44-45
    DOI: 10.1016/j.chaos.2017.03.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917300814
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.03.028?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Narahari Achar, B.N. & Hanneken, John W. & Clarke, T., 2002. "Response characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 275-288.
    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. Mehvish Fazal Ur Rehman & Yongyi Gu & Wenjun Yuan, 2020. "Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    2. Li, Wei & Huang, Dongmei & Zhang, Meiting & Trisovic, Natasa & Zhao, Junfeng, 2019. "Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 30-38.
    3. Sahadevan, R. & Prakash, P., 2017. "On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 107-120.

    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. Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
    2. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    3. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Muhammad Nadeem & Yahya Alsayaad, 2023. "A New Study for the Investigation of Nonlinear Fractional Drinfeld–Sokolov–Wilson Equation," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    5. Jun-Sheng Duan, 2013. "The Periodic Solution of Fractional Oscillation Equation with Periodic Input," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    6. Shabaz Jalil Mohammedfaeq & Miran Bayan Mohammed Amin & Dashne Chapuk Zahir & Shazad Shawki Ahmed, 2025. "An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    7. Yusuf Pandir & Tolga Akturk & Yusuf Gurefe & Hussain Juya, 2023. "The Modified Exponential Function Method for Beta Time Fractional Biswas‐Arshed Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    8. Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.
    9. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    10. Alam, M. Shamsul & Huq, M. Ashraful & Hasan, M. Kamrul & Rahman, M. Saifur, 2021. "A new technique for solving a class of strongly nonlinear oscillatory equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
    12. Tian, Yan & Zhong, Lin-Feng & He, Gui-Tian & Yu, Tao & Luo, Mao-Kang & Stanley, H. Eugene, 2018. "The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 845-856.
    13. Damarla, Seshu Kumar & Kundu, Madhusree, 2015. "Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 189-203.
    14. İbrahim Avcı & Nazim I. Mahmudov, 2020. "Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    15. Süleyman Öğrekçi, 2015. "Generalized Taylor Series Method for Solving Nonlinear Fractional Differential Equations with Modified Riemann‐Liouville Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    16. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    17. 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.
    18. Drozdov, A.D., 2007. "Fractional oscillator driven by a Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 237-245.
    19. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
    20. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    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:eee:chsofr:v:98:y:2017:i:c:p:44-45. 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.