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Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model

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  • Sabir, Zulqurnain
  • Said, Salem Ben
  • Baleanu, Dumitru

Abstract

The aim of this research is to present an investigation based on the fractional derivatives and perturbation factors for the novel singular system. This study also presents a novel design of the fractional perturbed singular system by using the conventional Lane-Emden form together with the features of fractional order values, singular points, perturbed terms and shape factors. An analysis based on the fractional order derivative and perturbation factors is provided using the novel singular form of the Lane-Emden system in two different ways with three different variations. The numerical representations based on the novel design of the fractional perturbed singular system are presented through the Meyer wavelet neural networks (MWNNs). The optimization is performed by using the hybrid efficiency of the global swarming particle swarm optimization (PSO) scheme along with the local interior-point algorithm (IPA). The modeling through the MWNN is signified through the novel fractional perturbed singular system through the mean square error along with the PSOIPA optimization. The exactness, verification, endorsement and excellence of the novel fractional perturbed singular system are authenticated through the comparison of the obtained and the true solutions. The reliability of the stochastic procedure is performed by using the statistical measures with a large domain of the dataset to analyze the fractional derivatives and perturbation factors for the novel singular system.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008396
    DOI: 10.1016/j.chaos.2022.112660
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    References listed on IDEAS

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    1. 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.
    2. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Altamirano, Gilder Cieza & Zhang, Yu-Dong & Le, Dac-Nhuong, 2021. "Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 87-101.
    4. Anwarud Din & Yongjin Li & Faiz Muhammad Khan & Zia Ullah Khan & Peijiang Liu, 2022. "On Analysis Of Fractional Order Mathematical Model Of Hepatitis B Using Atangana–Baleanu Caputo (Abc) Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-18, February.
    5. Jakub Horak & Jaromir Vrbka & Petr Suler, 2020. "Support Vector Machine Methods and Artificial Neural Networks Used for the Development of Bankruptcy Prediction Models and their Comparison," JRFM, MDPI, vol. 13(3), pages 1-15, March.
    6. Nida Shahid & Tim Rappon & Whitney Berta, 2019. "Applications of artificial neural networks in health care organizational decision-making: A scoping review," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-22, February.
    7. Spyridon Pougkakiotis & Jacek Gondzio, 2022. "An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 97-129, January.
    8. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    9. Ding, Yanming & Zhang, Wenlong & Yu, Lei & Lu, Kaihua, 2019. "The accuracy and efficiency of GA and PSO optimization schemes on estimating reaction kinetic parameters of biomass pyrolysis," Energy, Elsevier, vol. 176(C), pages 582-588.
    10. Amr Elsonbaty & Zulqurnain Sabir & Rajagopalan Ramaswamy & Waleed Adel, 2021. "Dynamical Analysis Of A Novel Discrete Fractional Sitrs Model For Covid-19," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-15, December.
    11. Zulqurnain Sabir & Hatıra Günerhan & Juan L. G. Guirao, 2020. "On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, February.
    12. Izadi, Mohammad, 2021. "A discontinuous finite element approximation to singular Lane-Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    13. Badenbroek, Riley, 2021. "Interior point methods and simulated annealing for nonsymmetric conic optimization," Other publications TiSEM 4374ab25-fdb5-4e6e-a198-6, Tilburg University, School of Economics and Management.
    14. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Khalique, Chaudry Masood & Unlu, Canan, 2021. "Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 799-812.
    15. 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.
    16. Guanbin Gao & Fei Liu & Hongjun San & Xing Wu & Wen Wang, 2018. "Hybrid Optimal Kinematic Parameter Identification for an Industrial Robot Based on BPNN-PSO," Complexity, Hindawi, vol. 2018, pages 1-11, July.
    17. Zulqurnain Sabir & Muhammad Umar & Muhammad Asif Zahoor Raja & Dumitru Baleanu, 2021. "Applications Of Gudermannian Neural Network For Solving The Sitr Fractal System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-20, December.
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