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Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS

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Abstract

The present study is related to design a novel multi-fractional multi-singular Lane–Emden model (MFMS-LEM) by keeping the ideas of the literature LEM and by extension of the work of doubly singular multi-fractional LEM. This mathematical novel MFMS-LEM is numerically treated by applying the fractional Meyer neuro-evolution intelligent solver (FMNEICS). The optimization is performed using the mutual heuristics of fractional Mayer wavelet neural networks (FMW-NN), the global search aptitude of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e., FMW-NN-GAIPA. The derivation steps, details of the singular points, fractional terms, shape factors and singular points are also provided. The modeling strength of MW-NN is implemented to characterize the novel model in the sagacity of mean squared error of objective function and network optimization is performed with the integrated capability of GAIPA. The authentication, perfection and verification of FMNEICS is checked for three diverse cases of the novel model which are conventional via relative studies through the reference solutions based on accuracy, stability, robustness and convergence procedures. Furthermore, the explanations via the statistical measures validate the value of the designed stochastic solver FMW-NN-GAIPA.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan

    Zulqurnain Sabir

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, R.O.C.

    Muhammad Asif Zahoor Raja

  3. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203, Cartagena, Spain

    Juan L. G. Guirao

  4. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Juan L. G. Guirao & Tareq Saeed

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  1. Zulqurnain Sabir
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  2. Muhammad Asif Zahoor Raja
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Sabir, Z., Raja, M.A.Z., Guirao, J.L.G. et al. Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS. Neural Comput & Applic 33, 17287–17302 (2021). https://doi.org/10.1007/s00521-021-06318-7

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