IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3792-d1232457.html
   My bibliography  Save this article

Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System

Author

Listed:
  • Zulqurnain Sabir

    (Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan
    Department of Computer Science and Mathematics, Lebanese American University, Beirut 1401, Lebanon)

  • Atef F. Hashem

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
    Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Beni-Suef 62514, Egypt)

  • Adnène Arbi

    (Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunis 2078, Tunisia
    Department of Advanced Sciences and Technologies at National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Hammam-Chott 1164, Tunisia)

  • Mohamed A. Abdelkawy

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
    Department of Mathematics and Information Science, Faculty of Science, Beni-Suef University, Beni-Suef 62514, Egypt)

Abstract

The present work provides the numerical solutions of the mathematical model based on the fractional-order Layla and Majnun model (MFLMM). A soft computing stochastic-based Bayesian regularization neural network approach (BRNNA) is provided to investigate the numerical accomplishments of the MFLMM. The nonlinear system is classified into two dynamics, whereas the correctness of the BRNNA is observed through the comparison of results. Furthermore, the reducible performance of the absolute error improves the exactitude of the computational BRNNA. Twenty neurons have been chosen, along with the data statics of training 74% and 13%, for both authorization and testing. The consistency of the designed BRNNA is demonstrated using the correlation/regression, error histograms, and transition of state values in order to solve the MFLMM.

Suggested Citation

  • Zulqurnain Sabir & Atef F. Hashem & Adnène Arbi & Mohamed A. Abdelkawy, 2023. "Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System," Mathematics, MDPI, vol. 11(17), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3792-:d:1232457
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3792/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3792/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zulqurnain Sabir & Dumitru Baleanu & Muhammad Asif Zahoor Raja & Ali S. Alshomrani & Evren Hincal, 2023. "Computational Performances Of Morlet Wavelet Neural Network For Solving A Nonlinear Dynamic Based On The Mathematical Model Of The Affection Of Layla And Majnun," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-18.
    2. Liao, Xiaofeng & Ran, Jiouhong, 2007. "Hopf bifurcation in love dynamical models with nonlinear couples and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 853-865.
    3. Mahmoud, Gamal M. & Aly, Shaban A.H., 2000. "On periodic solutions of parametrically excited complex non-linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 390-404.
    4. Juan L.G. Guirao & Zulqurnain Sabir & Tareq Saeed, 2020. "Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, August.
    5. Adiqa Kausar Kiani & Wasim Ullah Khan & Muhammad Asif Zahoor Raja & Yigang He & Zulqurnain Sabir & Muhammad Shoaib, 2021. "Intelligent Backpropagation Networks with Bayesian Regularization for Mathematical Models of Environmental Economic Systems," Sustainability, MDPI, vol. 13(17), pages 1-19, August.
    6. Zulqurnain Sabir & Juan L. G. Guirao, 2023. "A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    7. Amr Elsonbaty & Zulqurnain Sabir & Rajagopalan Ramaswamy & Waleed Adel, 2021. "Dynamical Analysis Of A Novel Discrete Fractional Sitrs Model For Covid-19," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-15, December.
    8. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(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. Zulqurnain Sabir & Juan L. G. Guirao, 2023. "A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    2. Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2021. "Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense," Mathematics, MDPI, vol. 9(19), pages 1-21, September.
    3. Kamal Abdelrahim Mohamed Shuka & Wang Ke & Mohammad Sohail Nazar & Ghali Abdullahi Abubakar & AmirReza Shahtahamssebi, 2022. "Impact of Hydrological Infrastructure Projects on Land Use/Cover and Socioeconomic Development in Arid Regions—Evidence from the Upper Atbara and Setit Dam Complex, Kassala, Eastern Sudan," Sustainability, MDPI, vol. 14(6), pages 1-23, March.
    4. Muhammad Umar & Zulqurnain Sabir & Muhammad Asif Zahoor Raja & Shumaila Javeed & Hijaz Ahmad & Sayed K. Elagen & Ahmed Khames, 2021. "Numerical Investigations through ANNs for Solving COVID-19 Model," IJERPH, MDPI, vol. 18(22), pages 1-15, November.
    5. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Li, Wei & Xu, Wei & Zhao, Junfeng & Wu, Haibo, 2007. "The study on stationary solution of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 465-472.
    7. Xu, Yong & Xu, Wei & Mahmoud, Gamal M, 2004. "On a complex beam–beam interaction model with random forcing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 347-360.
    8. Xu, Yong & Xu, Wei & Mahmoud, Gamal M., 2008. "On a complex Duffing system with random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 126-132.
    9. 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).
    10. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    11. Xu, Yong & Gu, Rencai & Zhang, Huiqing, 2011. "Effects of random noise in a dynamical model of love," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 490-497.
    12. Xu, Yong & Zhang, Huiqing & Xu, Wei, 2007. "On stochastic complex beam–beam interaction models with Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 259-272.
    13. Mohammad Izadi & Mahmood Parsamanesh & Waleed Adel, 2022. "Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System," Mathematics, MDPI, vol. 10(23), pages 1-26, December.
    14. Liu, Yifan & Cai, Jiazhi & Xu, Haowen & Shan, Minghe & Gao, Qingbin, 2023. "Stability and Hopf bifurcation of a love model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 558-580.
    15. JI, Conghuan & QIAO, Yuanhua & MIAO, Jun & DUAN, Lijuan, 2018. "Stability and Hopf bifurcation analysis of a complex-valued Wilson–Cowan neural network with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 45-61.
    16. Pei, Xin & Zhan, Xiu-Xiu & Jin, Zhen, 2017. "Application of pair approximation method to modeling and analysis of a marriage network," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 280-293.
    17. Songyue Yu & Baoqiang Yan, 2022. "Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations," Mathematics, MDPI, vol. 10(12), pages 1-19, June.
    18. Xu, Wei & Liang, Yingjie & Chen, Wen & Wang, Fajie, 2020. "Recent advances of stretched Gaussian distribution underlying Hausdorff fractal distance and its applications in fitting stretched Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    19. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.
    20. Cveticanin, L., 2003. "Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 83-94.

    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:gam:jmathe:v:11:y:2023:i:17:p:3792-:d:1232457. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.