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A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations

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  • Sivalingam, S M
  • Kumar, Pushpendra
  • Trinh, Hieu
  • Govindaraj, V.

Abstract

This paper proposes a novel L1-based predictor–corrector method for the fractional differential equations involving generalized-Caputo type derivative. A decomposition scheme is used to obtain the three-point predictor–corrector formula. The error and stability of the proposed method are given in detail. A computer virus and a five-dimensional Hopfield neural network models are solved using the proposed approach.

Suggested Citation

  • Sivalingam, S M & Kumar, Pushpendra & Trinh, Hieu & Govindaraj, V., 2024. "A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 462-480.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:462-480
    DOI: 10.1016/j.matcom.2024.01.017
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    1. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Kumar, Pushpendra & Vellappandi, M. & Khan, Zareen A. & S M, Sivalingam & Kaziboni, Anthony & Govindaraj, V., 2023. "A case study of monkeypox disease in the United States using mathematical modeling with real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 444-465.
    3. S M, Sivalingam & Kumar, Pushpendra & Govindaraj, V., 2023. "A novel numerical scheme for fractional differential equations using extreme learning machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    4. Zeng, Shengda & Baleanu, Dumitru & Bai, Yunru & Wu, Guocheng, 2017. "Fractional differential equations of Caputo–Katugampola type and numerical solutions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 549-554.
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. S M, Sivalingam & Kumar, Pushpendra & Govindaraj, Venkatesan, 2023. "A neural networks-based numerical method for the generalized Caputo-type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 302-323.
    7. 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).
    8. Jhinga, Aman & Daftardar-Gejji, Varsha, 2018. "A new finite-difference predictor-corrector method for fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 418-432.
    9. Vedat Suat Erturk & A.K. Alomari & Pushpendra Kumar & Marina Murillo-Arcila & Sundarapandian Vaidyanathan, 2022. "Analytic Solution for the Strongly Nonlinear Multi-Order Fractional Version of a BVP Occurring in Chemical Reactor Theory," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-9, June.
    10. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    12. Chen, Mengxin & Srivastava, Hari Mohan, 2023. "Stability of bifurcating solution of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.
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    Cited by:

    1. Liu, Hanjie & Zhu, Yuanguo, 2024. "Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 13-28.

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    More about this item

    Keywords

    L1 difference scheme; Stability; Error estimation; Generalized-Caputo derivative;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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