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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
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    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. 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.
    4. 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.
    5. 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.
    6. 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.
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    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).
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