RETRACTED ARTICLE: A fractional order nonlinear model of the love story of Layla and Majnun

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.

Swarm-optimized numerical investigation of Dengue Fever Model

“…Eq. (26)(27) presents the solution for case 1 and case 2. One can conclude that both GA-SQM with log sigmoid and the proposed MHW-SIRSLFFADNN-PSO-SQP solved the system accurately.…”

“…The nonlinear Lienard differential Model is also solved by the ANN-based solver [8]. ANN-based numerical solvers are also widely used to solve the nonlinear physical problem for instance, predator pre-model [9], lane Emden Model [10,11], film flow model [12], mass and heat transfer model [13], short-term hydrothermal coordination [14], large scale system [15], Emden-Fowler problem [16], life Cycle Optimization problem [17], Flierl equations [18,19], heat condition model [13,20], Singular Periodic boundary problem [21], prey-Predictive system [9,22], Smoke Problem [23], nervous stomach model [24], Engineering problems [25], Transport system [26], the Love story of Layle [27], and the monkeypox systems [28,29].…”

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

“…µ b < 0 and µ d < 0 are the emotions of real love. The simplified form of system (1) using the complex forms, i.e., M = iM i + M r and L = iL i + L r is given as [31,32]:…”

A neural network computational structure for the fractional order breast cancer model

“…The stochastic process has been derived before to solve various kind of the mathematical model, but the solutions of the FKBC model have been presented first time with the implementation of this scheme. Currently, the neural network-based procedures have been used to solve functional form of singular models 29 , hepatitis virus models 30 , bone remodeling model 31 , fractional vector-host diseased model 32 , SIRC epidemic model 33 , Zika virus model 34 , breathing transmission system 35 , thermal explosion model 36 , Rabinovich–Fabrikant system 37 , Layla and Majnun model 38 and food chain model 39 .…”