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Search Results (3)

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Keywords = Layla and Majnun

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13 pages, 2841 KB  
Article
Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System
by Zulqurnain Sabir, Atef F. Hashem, Adnène Arbi and Mohamed A. Abdelkawy
Mathematics 2023, 11(17), 3792; https://doi.org/10.3390/math11173792 - 4 Sep 2023
Cited by 17 | Viewed by 1753
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 [...] Read more.
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. Full article
(This article belongs to the Section C2: Dynamical Systems)
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15 pages, 981 KB  
Article
Complex-Variable Dynamic System of Layla and Majnun Model with Analytic Solutions
by Ibtisam Aldawish and Rabha W. Ibrahim
Symmetry 2023, 15(8), 1557; https://doi.org/10.3390/sym15081557 - 9 Aug 2023
Cited by 1 | Viewed by 1436
Abstract
A complex Layla and Majnun model system (CLMMS) is suggested in this study for a complex variable in the open-unit disk. Analytic solutions are discovered by using a technique of bounded turning functions. The set of necessary conditions is illustrated involving some special [...] Read more.
A complex Layla and Majnun model system (CLMMS) is suggested in this study for a complex variable in the open-unit disk. Analytic solutions are discovered by using a technique of bounded turning functions. The set of necessary conditions is illustrated involving some special cases. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Functional Equations)
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14 pages, 2606 KB  
Article
A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story
by Zulqurnain Sabir and Juan L. G. Guirao
Mathematics 2023, 11(4), 835; https://doi.org/10.3390/math11040835 - 7 Feb 2023
Cited by 16 | Viewed by 2383
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 [...] Read more.
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. Full article
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