IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v537y2020ics0378437119315560.html
   My bibliography  Save this article

Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation

Author

Listed:
  • Zhao, Dazhi
  • Yu, Guozhu
  • Tian, Yan

Abstract

Nonlinear evolution equations (NEEs) are very important partial differential equations in nonlinear physics, optics, and engineering. In this article, we apply the residual power series (RPS) method to the initial value problem of the nonlinear spatial conformable fractional evolution equations. Coefficients of the analytic solution are computed by recursive formulae and the famous nonlinear spatial conformable fractional Fisher equation is taken as an example to verify this method. Direct computations demonstrate the correctness of the recursive formulae. Meanwhile, the recursive formulae can be easily implemented by mathematical software.

Suggested Citation

  • Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315560
    DOI: 10.1016/j.physa.2019.122735
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119315560
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122735?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. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    2. Az-Zo’bi, Emad A. & Yıldırım, Ahmet & AlZoubi, Wael A., 2019. "The residual power series method for the one-dimensional unsteady flow of a van der Waals gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 188-196.
    3. Zhao, Dazhi & Pan, Xueqin & Luo, Maokang, 2018. "A new framework for multivariate general conformable fractional calculus and potential applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 271-280.
    4. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
    5. Alquran, Marwan & Al-Khaled, Kamel & Sardar, Tridip & Chattopadhyay, Joydev, 2015. "Revisited Fisher’s equation in a new outlook: A fractional derivative approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 81-93.
    6. Zhao, Dazhi & Luo, Maokang, 2019. "Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 531-544.
    7. Zhang, Sheng, 2008. "Application of Exp-function method to high-dimensional nonlinear evolution equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 270-276.
    8. Lin, Lifeng & Wang, Huiqi & Ma, Hong, 2019. "Directed transport properties of double-headed molecular motors with balanced cargo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 270-279.
    9. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    10. Zhao, Dazhi & Luo, Maokang, 2019. "Supplementary remark to ‘Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds’ [Applied Mathem," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 175-176.
    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. Zu, Chuanjin & Gao, Yanming & Yu, Xiangyang, 2021. "Time fractional evolution of a single quantum state and entangled state," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    3. Muhammed I. Syam, 2017. "Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method," Complexity, Hindawi, vol. 2017, pages 1-6, August.
    4. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Han, Yuxin & Huang, Xin & Gu, Wei & Zheng, Bolong, 2023. "Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. Thabet, Hayman & Kendre, Subhash, 2018. "Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 238-245.
    7. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    8. Lin, Lifeng & Lin, Tianzhen & Zhang, Ruoqi & Wang, Huiqi, 2023. "Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    9. Zhao, Dazhi & Pan, Xueqin & Luo, Maokang, 2018. "A new framework for multivariate general conformable fractional calculus and potential applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 271-280.
    10. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    11. Korkmaz, Alper, 2017. "Exact solutions of space-time fractional EW and modified EW equations," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 132-138.
    12. Khaled, Khachnaoui, 2021. "Nehari type solutions for fractional Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    13. Xiao, Guanli & Wang, JinRong & O’Regan, Donal, 2020. "Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    14. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
    15. Tian, Yan & He, Guitian & Liu, Zhibin & Zhong, Linfeng & Yang, Xinping & Stanley, H. Eugene & Tu, Zhe, 2021. "The impact of memory effect on resonance behavior in a fractional oscillator with small time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    16. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
    17. Erbaş, Barış & Yusufoğlu, Elçin, 2009. "Exp-function method for constructing exact solutions of Sharma–Tasso–Olver equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2326-2330.
    18. Muhammad Samraiz & Ahsan Mehmood & Saima Naheed & Gauhar Rahman & Artion Kashuri & Kamsing Nonlaopon, 2022. "On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function," Mathematics, MDPI, vol. 10(21), pages 1-19, October.
    19. Wei, Dongmei & Liu, Hailing & Li, Yongmei & Wan, Linchun & Qin, Sujuan & Wen, Qiaoyan & Gao, Fei, 2024. "Non-Markovian dynamics of time-fractional open quantum systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    20. Khani, F., 2009. "Analytic study on the higher order Ito equations: New solitary wave solutions using the Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2128-2134.

    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:phsmap:v:537:y:2020:i:c:s0378437119315560. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.