IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p835-d1060038.html
   My bibliography  Save this article

A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story

Author

Listed:
  • Zulqurnain Sabir

    (Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan
    Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon)

  • Juan L. G. Guirao

    (Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain
    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

The current study shows the numerical performances of the fractional order mathematical model based on the Majnun and Layla (FO-MML) romantic story. The stochastic computing numerical scheme based on the scaled conjugate gradient neural networks (SCGNNs) is presented to solve the FO-MML. The purpose of providing the solutions of the fractional derivatives is to achieve more accurate and realistic performances of the FO-MML romantic story model. The mathematical model is divided into four dynamics, while the exactness is authenticated through the comparison of obtained and reference Adam results. Moreover, the negligible absolute error enhances the accuracy of the stochastic scheme. Fourteen numbers of neurons have been taken and the information statics are divided into authorization, training, and testing, which are divided into 12%, 77% and 11%, respectively. The reliability, capability, and accuracy of the stochastic SCGNNs is performed through the stochastic procedures using the regression, error histograms, correlation, and state transitions for solving the mathematical model.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:835-:d:1060038
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/835/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/835/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. 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.
    5. Umar, Muhammad & Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Aguilar, J.F. Gómez & Amin, Fazli & Shoaib, Muhammad, 2021. "Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 241-253.
    6. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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 & 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.
    2. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    3. 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.
    4. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    5. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. 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).
    7. 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.
    8. 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.
    9. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-23, August.
    10. 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.
    11. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. 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.
    13. Belmahi, Naziha & Shawagfeh, Nabil, 2021. "A new mathematical model for the glycolysis phenomenon involving Caputo fractional derivative: Well posedness, stability and bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Zulqurnain Sabir & Salem Ben Said & Juan L. G. Guirao, 2023. "A Radial Basis Scale Conjugate Gradient Deep Neural Network for the Monkeypox Transmission System," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    20. Shoaib, Muhammad & Abbasi, Aqsa Zafar & Raja, Muhammad Asif Zahoor & Nisar, Kottakkaran Sooppy, 2022. "A design of predictive computational network for the analysis of fractional epidemical predictor-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:4:p:835-:d:1060038. 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.