IDEAS home Printed from https://ideas.repec.org/a/wly/complx/v2022y2022i1n4141988.html

Numerical Investigation of the Nonlinear Coupled Fractional Massive Thirring Equation Using Two‐Scale Approach

Author

Listed:
  • Jinxing Liu
  • Muhammad Nadeem
  • Mustafa Habib
  • Shazia Karim
  • Harun Or Roshid

Abstract

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform (FCT). This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method (HPM) is employed to tackle the nonlinear terms in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two‐scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering.

Suggested Citation

  • Jinxing Liu & Muhammad Nadeem & Mustafa Habib & Shazia Karim & Harun Or Roshid, 2022. "Numerical Investigation of the Nonlinear Coupled Fractional Massive Thirring Equation Using Two‐Scale Approach," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4141988
    DOI: 10.1155/2022/4141988
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/4141988
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/4141988?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. Mohamed R. Ali, 2019. "A Truncation Method for Solving the Time‐Fractional Benjamin‐Ono Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    2. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    3. Mohamed R. Ali, 2019. "A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-7, May.
    4. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    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. Mohamed R. Ali & Wen-Xiu Ma, 2019. "New Exact Solutions of Nonlinear (3 + 1)‐Dimensional Boiti‐Leon‐Manna‐Pempinelli Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    2. Wilson Osafo Apeanti & David Yaro & Saviour Worlanyo Akuamoah, 2025. "Solitary Wave Solutions and Modulation Instability of First‐ and Second‐Order Benjamin–Ono Fluid Dynamics Models With Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    3. F. Ghomanjani & A. V. Kamyad & A. Kılıçman, 2013. "Bezier Curves Method for Fourth‐Order Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    5. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
    6. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Qinghao Zhu & Jianming Qi, 2022. "Exact Solutions of the Nonlinear Space‐Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    8. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    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 synchronization using optimized fractional order sli," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Fang Wang & Zhen-hai Liu & Jing Li, 2013. "Complete Controllability of Fractional Neutral Differential Systems in Abstract Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    12. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    13. 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.
    14. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
    15. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    16. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
    17. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    18. Maneesha Gupta & Richa Yadav, 2013. "Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts," Journal of Optimization, Hindawi, vol. 2013, pages 1-11, June.
    19. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    20. Serik Aitzhanov & Kymbat Bekenayeva & Zamira Abdikalikova, 2023. "Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator," Mathematics, MDPI, vol. 11(18), pages 1-12, September.

    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:complx:v:2022:y:2022:i:1:n:4141988. 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/8503 .

    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.