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Design Of Neuro-Swarming Heuristic Solver For Multi-Pantograph Singular Delay Differential Equation

Author

Listed:
  • ZULQURNAIN SABIR

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

  • 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)

  • JUAN L. G. GUIRAO

    (*Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina 30203-Cartagena, Spain)

Abstract

This research work is to design a neural-swarming heuristic procedure for numerical investigations of Singular Multi-Pantograph Delay Differential (SMP-DD) equation by applying the function approximation aptitude of Artificial Neural Networks (ANNs) optimized efficient swarming mechanism based on Particle Swarm Optimization (PSO) integrated with convex optimization with Active Set (AS) algorithm for rapid refinements, named as ANN-PSO-AS. A merit function (MF) on mean squared error sense is designed by using the differential ANN models and boundary condition. The optimization of this MF is executed with the global PSO and local search AS approaches. The planned ANN-PSO-AS approach is instigated for three different SMP-DD model-based equations. The assessment with available standard results relieved the effectiveness, robustness and precision that is further authenticated through statistical investigations of Variance Account For, Root Mean Squared Error, Semi-Interquartile Range and Theil’s inequality coefficient performances.

Suggested Citation

  • Zulqurnain Sabir & Dumitru Baleanu & Muhammad Asif Zahoor Raja & Juan L. G. Guirao, 2021. "Design Of Neuro-Swarming Heuristic Solver For Multi-Pantograph Singular Delay Differential Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-16, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21400223
    DOI: 10.1142/S0218348X21400223
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    Cited by:

    1. 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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