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A fractional order nonlinear model of the love story of Layla and Majnun

2023; Nature Portfolio; Volume: 13; Issue: 1 Linguagem: Inglês

10.1038/s41598-023-32497-5

2045-2322

Zulqurnain Sabir, Salem Ben Saïd,

Advanced Control Systems Design

Abstract In this study, a fractional order mathematical model using the romantic relations of the Layla and Majnun is numerically simulated by the Levenberg–Marquardt backpropagation neural networks. The fractional order derivatives provide more realistic solutions as compared to integer order derivatives of the mathematical model based on the romantic relationship of the Layla and Majnun. The mathematical formulation of this model has four categories that are based on the system of nonlinear equations. The exactness of the stochastic scheme is observed for solving the romantic mathematical system using the comparison of attained and Adam results. The data for testing, authorization, and training is provided as 15%, 75% and 10%, along with the twelve numbers of hidden neurons. Furthermore, the reducible value of the absolute error improves the accuracy of the designed stochastic solver. To prove the reliability of scheme, the numerical measures are presented using correlations, error histograms, state transitions, and regression.