IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v131y2020ics096007791930462x.html
   My bibliography  Save this article

Spline collocation methods for systems of fuzzy fractional differential equations

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791930462X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109510?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. S. K. Elagan & Dumitru Baleanu, 2012. "Set-Valued Fixed-Point Theorems for Generalized Contractive Mappings on Fuzzy Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, May.
    2. T. Allahviranloo & S. Salahshour & M. Homayoun-nejad & D. Baleanu, 2013. "General Solutions of Fully Fuzzy Linear Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
    3. Ali Ahmadian & Mohamed Suleiman & Soheil Salahshour, 2013. "An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-29, June.
    4. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    5. Baleanu, D. & Shiri, B., 2018. "Collocation methods for fractional differential equations involving non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 136-145.
    6. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.
    7. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    8. Shiri, B. & Baleanu, D., 2019. "System of fractional differential algebraic equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 203-212.
    9. 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.
    10. Azizollah Babakhani & Dumitru Baleanu, 2012. "Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    3. Ariza-Hernandez, Francisco J. & Martin-Alvarez, Luis M. & Arciga-Alejandre, Martin P. & Sanchez-Ortiz, Jorge, 2021. "Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. 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).
    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.

    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. Abdelkawy, M.A. & Lopes, António M. & Babatin, Mohammed M., 2020. "Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. A. Rufián-Lizana & Y. Chalco-Cano & G. Ruiz-Garzón & H. Román-Flores, 2014. "On some characterizations of preinvex fuzzy mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 771-783, July.
    3. Thanh-Lam Nguyen, 2017. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews," Complexity, Hindawi, vol. 2017, pages 1-13, July.
    4. Ariza-Hernandez, Francisco J. & Martin-Alvarez, Luis M. & Arciga-Alejandre, Martin P. & Sanchez-Ortiz, Jorge, 2021. "Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    6. Eman Hussain & Ayad Ali, 2013. "Homotopy Analysis Method for Solving Fuzzy Integro-Differential Equations," Modern Applied Science, Canadian Center of Science and Education, vol. 7(3), pages 1-15, March.
    7. Nguyen Dinh Phu, 2016. "On Nonlocal Initial Problems for Fuzzy Differential Equations and Environmental Pollution Problems," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 2(8), pages 77-92, 08-2016.
    8. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    9. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    10. Dassios, Ioannis & Tzounas, Georgios & Liu, Muyang & Milano, Federico, 2022. "Singular over-determined systems of linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 396-412.
    11. Ho Vu, 2017. "Random Fuzzy Differential Equations with Impulses," Complexity, Hindawi, vol. 2017, pages 1-11, June.
    12. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    13. Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Liao, Xiaozhong & Wang, Yong & Yu, Donghui & Lin, Da & Ran, Manjie & Ruan, Pengbo, 2023. "Modeling and analysis of Buck-Boost converter with non-singular fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Harb, Ahmad M. & Smadi, Issam A., 2009. "Tracking control of DC motors via mimo nonlinear fuzzy control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 702-710.
    16. Fabio Tramontana & Laura Gardini, 2021. "Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-15, December.
    17. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
    18. Hoang Viet Long & Haifa Bin Jebreen & Y. Chalco-Cano, 2020. "A New Continuous-Discrete Fuzzy Model and Its Application in Finance," Mathematics, MDPI, vol. 8(10), pages 1-15, October.
    19. Hamzeh Zureigat & Mohammed Al-Smadi & Areen Al-Khateeb & Shrideh Al-Omari & Sharifah Alhazmi, 2023. "Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells," IJERPH, MDPI, vol. 20(4), pages 1-13, February.
    20. Su, Guangwang & Lu, Liang & Tang, Bo & Liu, Zhenhai, 2020. "Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems," Applied Mathematics and Computation, Elsevier, vol. 378(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:131:y:2020:i:c:s096007791930462x. 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.