IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2022y2022i1n1534067.html

The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Author

Listed:
  • Farah M. Al-Askar
  • Wael W. Mohammed

Abstract

This article considers the stochastic fractional Radhakrishnan‐Kundu‐Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan‐Kundu‐Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

Suggested Citation

  • Farah M. Al-Askar & Wael W. Mohammed, 2022. "The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:1534067
    DOI: 10.1155/2022/1534067
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/1534067
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/1534067?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. Qura Tul Ain & T. Sathiyaraj & Shazia Karim & Muhammad Nadeem & Patrick Kandege Mwanakatwe & C. Rajivganthi, 2022. "ABC Fractional Derivative for the Alcohol Drinking Model using Two-Scale Fractal Dimension," Complexity, Hindawi, vol. 2022, pages 1-11, June.
    2. Khan, Aziz & Abdeljawad, Thabet & Gómez-Aguilar, J.F. & Khan, Hasib, 2020. "Dynamical study of fractional order mutualism parasitism food web module," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Farah M. Al-Askar & Wael W. Mohammed & Mohammad Alshammari & M. El-Morshedy, 2022. "Effects of the Wiener Process on the Solutions of the Stochastic Fractional Zakharov System," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    4. Anwarud Din & Yongjin Li & Faiz Muhammad Khan & Zia Ullah Khan & Peijiang Liu, 2022. "On Analysis Of Fractional Order Mathematical Model Of Hepatitis B Using Atangana–Baleanu Caputo (Abc) Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-18, February.
    5. Qura Tul Ain & T. Sathiyaraj & Shazia Karim & Muhammad Nadeem & Patrick Kandege Mwanakatwe, 2022. "ABC Fractional Derivative for the Alcohol Drinking Model using Two‐Scale Fractal Dimension," Complexity, John Wiley & Sons, vol. 2022(1).
    6. Wael W. Mohammed & Naveed Iqbal & Thongchai Botmart, 2022. "Additive Noise Effects on the Stabilization of Fractional-Space Diffusion Equation Solutions," Mathematics, MDPI, vol. 10(1), pages 1-14, January.
    7. Ain, Qura tul & Khan, Aziz & Ullah, Muhammad Irfan & Alqudah, Manar A. & Abdeljawad, Thabet, 2022. "On fractional impulsive system for methanol detoxification in human body," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Kangle Wang, 2022. "Fractal Solitary Wave Solutions For Fractal Nonlinear Dispersive Boussinesq-Like Models," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-8, June.
    9. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    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. Adnan Khan & M. Haris Mateen & Ali Akgül & Md. Shajib Ali, 2022. "The K Extended Laguerre Polynomials Involving Aαr,n,kxr Fr, r > 2," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    2. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Adel Elmandouh & Muneerah Al Nuwairan & M. M. El-Dessoky, 2025. "Nonlinear Dynamical Analysis and New Solutions of the Space-Fractional Stochastic Davey–Stewartson Equations for Nonlinear Water Waves," Mathematics, MDPI, vol. 13(5), pages 1-17, February.
    4. Chein-Shan Liu & Jiang-Ren Chang & Jian-Hung Shen & Yung-Wei Chen, 2022. "A Boundary Shape Function Method for Computing Eigenvalues and Eigenfunctions of Sturm–Liouville Problems," Mathematics, MDPI, vol. 10(19), pages 1-22, October.
    5. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Mrutyunjaya Sahoo & Snehashish Chakraverty, 2022. "Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    7. Abdulfatai Atte Momoh & Abubakar Audu & Déthié Dione & Inalegwu Michael Ali, 2023. "On the Optimal Control of Intervention Strategies for Hepatitis B Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2023(1).
    8. Singh, Harendra & Baleanu, Dumitru & Singh, Jagdev & Dutta, Hemen, 2021. "Computational study of fractional order smoking model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2024. "A novel SIRS epidemic model for two diseases incorporating treatment functions, media coverage, and three types of noise," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    11. Mashayekhi, S. & Sedaghat, S., 2021. "Fractional model of stem cell population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Ajay Kumar & Sara Salem Alzaid & Badr Saad T. Alkahtani & Sunil Kumar, 2022. "Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    13. Jirong Yang & Farkhanda Afzal & Perpetual Appiah, 2022. "ABC Fractional Derivative for Varicella‐Zoster Virus Using Two‐Scale Fractal Dimension Approach with Vaccination," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    14. Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    15. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Tariq Q. S. Abdullah & Gang Huang & Wadhah Al-Sadi & Yasser Aboelmagd & Wael Mobarak, 2024. "Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme," Mathematics, MDPI, vol. 12(15), pages 1-24, July.
    17. Qura Tul Ain & Muhammad Nadeem & Devendra Kumar & Mohd Asif Shah, 2023. "Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    18. Jiahua Fang & Muhammad Nadeem & Hanan A. Wahash, 2022. "A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    19. Abdelhamid Mohammed Djaouti & Muhammad Imran Liaqat, 2025. "Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations," Mathematics, MDPI, vol. 13(8), pages 1-23, April.
    20. Yaagoub, Zakaria & Allali, Karam, 2022. "Fractional HBV infection model with both cell-to-cell and virus-to-cell transmissions and adaptive immunity," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:jnlamp:v:2022:y:2022:i:1:n:1534067. 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/3197 .

    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.