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Spline collocation methods for systems of fuzzy fractional differential equations

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  • Alijani, Zahra
  • Baleanu, Dumitru
  • Shiri, Babak
  • Wu, Guo-Cheng

Abstract

In this paper, systems of fuzzy fractional differential equations with a lateral type of the Hukuhara derivative and the generalized Hukuhara derivative are numerically studied. Collocation method on discontinuous piecewise polynomial spaces is proposed. Convergence of the proposed method is analyzed. The superconvergent results on the graded mesh are studied. Examples are provided to support theoretical results. Finally, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application.

Suggested Citation

  • Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s096007791930462x
    DOI: 10.1016/j.chaos.2019.109510
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    References listed on IDEAS

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    8. Ferial Ghaemi & Robiah Yunus & Ali Ahmadian & Soheil Salahshour & Mohamed Suleiman & Shanti Faridah Saleh, 2013. "Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, September.
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    Cited by:

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    2. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. 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).
    4. Yanping Zheng & Hui Yang & Wenxia Wang, 2024. "Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval," Mathematics, MDPI, vol. 12(2), pages 1-15, January.
    5. Mohapatra, Dhabaleswar & Chakraverty, S., 2023. "Initial value problems in Type-2 fuzzy environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 230-242.

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