IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922008396.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922008396
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112660?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Naz, Sidra & Raja, Muhammad Asif Zahoor & Kausar, Aneela & Zameer, Aneela & Mehmood, Ammara & Shoaib, Muhammad, 2022. "Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 88-113.
    2. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. El-Mesady, A. & Elsonbaty, Amr & Adel, Waleed, 2022. "On nonlinear dynamics of a fractional order monkeypox virus model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Beata Gavurova & Sylvia Jencova & Radovan Bacik & Marta Miskufova & Stanislav Letkovsky, 2022. "Artificial intelligence in predicting the bankruptcy of non-financial corporations," Oeconomia Copernicana, Institute of Economic Research, vol. 13(4), pages 1215-1251, December.
    6. Rahman, Mati ur & Arfan, Muhammad & Shah, Kamal & Gómez-Aguilar, J.F., 2020. "Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Xu, Li & Li, Shengcai & Sun, Wanghu & Ma, Xin & Cao, Shuchao, 2020. "Combustion behaviors and characteristic parameters determination of sassafras wood under different heating conditions," Energy, Elsevier, vol. 203(C).
    8. Wu, C.B. & Guan, P.B. & Zhong, L.N. & Lv, J. & Hu, X.F. & Huang, G.H. & Li, C.C., 2020. "An optimized low-carbon production planning model for power industry in coal-dependent regions - A case study of Shandong, China," Energy, Elsevier, vol. 192(C).
    9. Xianhui Mao & Ankui Hu & Rui Zhao & Fei Wang & Mengkun Wu, 2023. "Evaluation and Application of Surrounding Rock Stability Based on an Improved Fuzzy Comprehensive Evaluation Method," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    10. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Julian Schiele & Thomas Koperna & Jens O. Brunner, 2021. "Predicting intensive care unit bed occupancy for integrated operating room scheduling via neural networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(1), pages 65-88, February.
    12. Muhammad Umar & Zulqurnain Sabir & Muhammad Asif Zahoor Raja & Shumaila Javeed & Hijaz Ahmad & Sayed K. Elagen & Ahmed Khames, 2021. "Numerical Investigations through ANNs for Solving COVID-19 Model," IJERPH, MDPI, vol. 18(22), pages 1-15, November.
    13. 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.
    14. Ding, Yanming & Chen, Wenlu & Zhang, Wenlong & Zhang, Xueting & Li, Changhai & Zhou, Ru & Miao, Fasheng, 2022. "Experimental and numerical simulation study of typical semi-transparent material pyrolysis with in-depth radiation based on micro and bench scales," Energy, Elsevier, vol. 258(C).
    15. Zou, Songchun & Zhao, Wanzhong, 2020. "Energy optimization strategy of vehicle DCS system based on APSO algorithm," Energy, Elsevier, vol. 208(C).
    16. Ndenda, J.P. & Njagarah, J.B.H. & Shaw, S., 2021. "Role of immunotherapy in tumor-immune interaction: Perspectives from fractional-order modelling and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    17. Muhammad Ali Qureshi & Najeeb Alam Khan, 2024. "Clown face in 3D chaotic system integrated with memristor electronics, DNA encryption and fractional calculus," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-16, May.
    18. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    19. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    20. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008396. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.