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FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems

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Abstract

The fractional neuro-evolution-based intelligent computing has substantial potential to solve fractional order systems represented with Lane–Emden equation arising in astrophysics including Newtonian self-gravitating, spherically symmetric and polytropic fluid. The present study aimed to present a neuro-swarm-based intelligent computing solver for the solution of nonlinear fractional Lane–Emden system (NFLES) using by exploitation of fractional Meyer wavelet artificial neural networks (FMW-ANNs) and global optimization mechanism of particle swarm optimization (PSO) combined with rapid local search of sequential quadratic programming (SQP), i.e., FMW-ANN-PSO-SQP. The motivation for the design of FMW-ANN-PSO-SQP intelligent computing comes with an objective of presenting an accurate, reliable, and viable framworks to deal with stiff nonlinear singular models represented with NFLES involving both fractional and integer derivative terms. The designed algorithm is tested for six different variants of NFLESs. The obtained numerical outcomes obtained by the proposed FMW-ANN-PSO-SQP are compared with the exact results to authenticate the correctness, efficacy, and viability, and these aspects are further endorsed statistical observations.

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Authors and Affiliations

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

    Zulqurnain Sabir & Muhammad Umar

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

    Muhammad Asif Zahoor Raja

  3. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Asif Zahoor Raja

  4. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shoaib

  5. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  6. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

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  1. Zulqurnain Sabir
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  2. Muhammad Asif Zahoor Raja
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  3. Muhammad Umar
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  5. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Sabir, Z., Raja, M.A.Z., Umar, M. et al. FMNSICS: Fractional Meyer neuro-swarm intelligent computing solver for nonlinear fractional Lane–Emden systems. Neural Comput & Applic 34, 4193–4206 (2022). https://doi.org/10.1007/s00521-021-06452-2

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