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Solution to the Bessel differential equation with interactive fuzzy boundary conditions

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Abstract

In this paper we deal with the fuzzy boundary value problem of the Bessel differential equation, whose boundary conditions are uncertain and given by linearly interactive fuzzy numbers. The Bessel differential equation can be considered in order to model wave and heat propagation problems. The fuzzy solution is obtained from the sup-J extension principle. We show that the sup-J extension provides proper fuzzy solution for the Bessel differential equation. In addition, we study the advantages of the proposed approach with others well known methods, such as the solutions based on the Zadeh extension principle and the solutions derived from the generalized Hukuhara derivative.

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Acknowledgements

This research was partially supported by CNPq under grants no. 306546/2017-5 and 313313/2020-2.

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Authors and Affiliations

  1. Center of Basic Science Teaching for Engineering, University Austral of Chile, Valdivia, Los Ríos, Chile

    Daniel Eduardo Sánchez

  2. Department of Mathematics, São Paulo State University, Rio Claro, São Paulo, Brazil

    Vinícius Francisco Wasques

  3. Department of Applied Mathematics, University of Campinas, Campinas, São Paulo, Brazil

    Estevão Esmi & Laécio Carvalho de Barros

  4. Ilum School of Science, Brazilian Center for Research in Energy and Materials, Campinas, São Paulo, Brazil

    Vinícius Francisco Wasques

Authors
  1. Daniel Eduardo Sánchez
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  2. Vinícius Francisco Wasques
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  3. Estevão Esmi
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  4. Laécio Carvalho de Barros
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Communicated by Anibal Tavares de Azevedo.

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Sánchez, D.E., Wasques, V.F., Esmi, E. et al. Solution to the Bessel differential equation with interactive fuzzy boundary conditions. Comp. Appl. Math. 41, 1 (2022). https://doi.org/10.1007/s40314-021-01695-0

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  • DOI: https://doi.org/10.1007/s40314-021-01695-0

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