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Applications of neural networks for the novel designed of nonlinear fractional seventh order singular system

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The purpose of this work is to design a novel nonlinear fractional seventh kind of singular (NSKS) Emden–Fowler model (EFM), i.e., NSKS-EFM together with its six categories. The novel design of NSKS-EFM is obtained with the use of typical EFM of the second kind. The shape factor and singular points detail is accessible for all six categories of the NSKS-EFM. The singular problems arise in the mathematical engineering problems, like as inverse models, creep or viscoelasticity problems. To check the correctness of the designed novel NSKS-EFM, three different cases of the first category will be solved by using the supervised neural networks (SNNs) together with the Levenberg–Marquardt backpropagation method (LMBM), i.e., SNNs-LMBM. A reference dataset based on the exact solutions with the SNNS-LMBM will be performed for each case of the novel NSKS-EFM. The obtained approximate solutions of all three cases of the first group based on the novel NSKS-EFM is available using the testing, training and verification procedures of the proposed NNs to summarize the mean square error (MSE) along with the LMBM. To check the efficiency, effectiveness, and correctness of the novel NSKS-EFM and the proposed SNNS-LMBM, the numerical investigations are obtainable using the comparative actions of MSE results, regression, error histograms and correlation.

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Correspondence to Mohamed R. Ali.

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Sabir, Z., Raja, M.A.Z., Nguyen, T.G. et al. Applications of neural networks for the novel designed of nonlinear fractional seventh order singular system. Eur. Phys. J. Spec. Top. 231, 1831–1845 (2022).

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