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Fractional Mayer Neuro-Swarm Heuristic Solver For Multi-Fractional Order Doubly Singular Model Based On Lane–Emden Equation

Author

Listed:
  • ZULQURNAIN SABIR

    (Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan)

  • MUHAMMAD ASIF ZAHOOR RAJA

    (��Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3 Douliou, Yunlin 64002, Taiwan, R.O.C.‡Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan)

  • DUMITRU BALEANU

    (�Department of Mathematics, Cankaya University, Ankara, Turkey¶Institute of Space Science, Magurele-Bucharest, Romania∥Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan)

Abstract

This research is related to present a novel fractional Mayer neuro-swarming intelligent solver for the numerical treatment of multi-fractional order doubly singular Lane–Emden (LE) equation using combined investigations of the Mayer wavelet (MW) neural networks (NNs) optimized by the global search effectiveness of particle swarm optimization (PSO) and interior-point (IP) method, i.e. MW-NN-PSOIP. The design of novel fractional Mayer neuro-swarming intelligent solver for multi-fractional order doubly singular LE equation is derived from the standard LE model and the shape factors; fractional order terms along with singular points are examined. The modeling based on the MW-NN strength is implemented to signify the multi-fractional order doubly singular LE model using the ability of mean squared error in terms of the merit function and the networks are optimized with the integrated capability of PSOIP scheme. The perfection, verification and validation of the fractional Mayer neuro-swarming intelligent solver for three different cases of the multi-fractional order doubly singular LE equation are recognized through comparative investigations from the reference results on different measures based on the convergence, robustness, stability and accuracy. Furthermore, the statics interpretations further validate the performance of the proposed fractional Mayer neuro-swarming intelligent solvers.

Suggested Citation

  • Zulqurnain Sabir & Muhammad Asif Zahoor Raja & Dumitru Baleanu, 2021. "Fractional Mayer Neuro-Swarm Heuristic Solver For Multi-Fractional Order Doubly Singular Model Based On Lane–Emden Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-15, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x2140017x
    DOI: 10.1142/S0218348X2140017X
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    Citations

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    Cited by:

    1. Umar, Muhammad & Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Baskonus, Haci Mehmet & Ali, Mohamed R. & Shah, Nehad Ali, 2023. "Heuristic computing with sequential quadratic programming for solving a nonlinear hepatitis B virus model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 234-248.
    2. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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