Browsing by Author "Babatin, M. M."

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Citation Count: 0
Design of stochastic neural networks for the fifth order system of singular engineering model
(Pergamon-elsevier Science Ltd, 2024) Sabir, Zulqurnain; Salahshour, Soheıl; Hashem, Atef F.; Abdelkawy, M. A.; Salahshour, Soheil; Umar, Muhammad
The current investigations provides a stochastic platform using the computational Levenberg-Marquardt Backpropagation (LMB) neural network (NN) approach, i.e., LMB-NN for solving the fifth order Emden-Fowler system (FOEFS) of equations. The singular models are always considered tough due to the singularity by using the traditional schemes, hence the stochastic solvers handle efficiently the singular point exactly at zero. The solution of four types of equations based on the FOEFS is presented by using the singularity and shape factor values. To calculate the approximate solutions of the FOEFS of equations, the training, validation and testing performances are used to reduce the mean square error. The selection of the training data is 70%, while testing and validation performances are used as 10% and 20%. The scheme's correctness is performed through the result's comparison along with the negligible absolute error performances for each example of the FOEFS. Moreover, the relative study through different investigations-based error histograms, and correlation update the efficacy of the scheme.
Citation Count: 0
A neural network computational procedure for the novel designed singular fifth order nonlinear system of multi-pantograph differential equations
(Elsevier, 2024) Bhat, Shahid Ahmad; Salahshour, Soheıl; Sabir, Zulqurnain; Babatin, M. M.; Hashem, Atef F.; Abdelkawy, M. A.; Salahshour, Soheil
The current investigations present the numerical solutions of the novel singular nonlinear fifth-order (SNFO) system of multi-pantograph differential model (SMPDM), i.e., SNFO-SMPDM. The novel SNFO-SMPDM is obtained using the sense of the second kind of typical Emden-Fowler and prediction differential models. The features of shape factor, pantograph along with singular points are provided for all four obtained classes of the SNFO-SMPDM. The extensive use of the singular models is observed in the engineering and mathematical systems, e.g., inverse systems and viscoelasticity or creep systems. For the correctness of the proposed novel SNFO-SMPDM, one case of each class is numerically handled by applying supervised neural networks (SNNs) along with the optimization of Levenberg-Marquardt backpropagation scheme (LMBS), i.e., SNNs-LMBS. A dataset using the traditional variational iteration scheme is designed to compare the proposed results of each case of SNFO-SMPDM. The obtained approximate solutions of each class using the novel SNFO-SMPDM are presented based on the training (80 %), authentication (10 %) and testing (10 %) measures to evaluate the mean square error. Fifteen numbers of neurons, and sigmoid activation function are used in this SNN process. To authenticate the competence, and precision of SNFO-SMPDM, the numerical simulations are accessible by applying the relative measures of regression, error histogram plots, and correlation.