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On fuzzy Laplace transform in linearly correlated fuzzy space

  • Fuzzy systems and their mathematics
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Abstract

In this manuscript, we present the notion of improper Riemann integral and develop a methodology to solve nth-order fuzzy initial value problems (FIVPs) via fuzzy Laplace transform for linearly correlated processes. Our approach translates a fuzzy differential equation (FDE) problem from the fuzzy number space to a well-established Banach space. In this new approach, it is not necessary to consider several cases due to switch points, and we do not need to use the Stacking theorem because the obtained solution is always a fuzzy number. In order to illustrate our approach, we present several examples comparing the obtained solutions with those produced by other methods.

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Acknowledgements

This research was partially supported by CNPq under grant no. \(313313/2020-2\), and CNPq under Grant No. \(306546/2017-5\).

Funding

This research was partially supported by CNPq under Grant No. \(313313/2020-2\), and CNPq under Grant No. \(306546/2017-5\).

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Authors and Affiliations

  1. Multidisciplinary Department, Federal University of São Paulo, Osasco, São Paulo, 06110295, Brazil

    Francielle Santo Pedro

  2. Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais, 37048395, Brazil

    Silvio Antônio Bueno Salgado

  3. Center of Basic Science Teaching for Engineering, University Austral of Chile, Valdivia, Street, 5110566, Valdivia, Los Ríos, Chile

    Daniel Eduardo Sánchez

  4. Department of Applied Mathematics, University of Campinas, Street, Campinas, São Paulo, 13083859, Brazil

    Estevão Esmi & Laécio Carvalho de Barros

Authors
  1. Francielle Santo Pedro
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  2. Silvio Antônio Bueno Salgado
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  3. Daniel Eduardo Sánchez
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  4. Estevão Esmi
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  5. Laécio Carvalho de Barros
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These authors contributed equally to this work.

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Correspondence to Francielle Santo Pedro.

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Pedro, F.S., Salgado, S.A.B., Sánchez, D.E. et al. On fuzzy Laplace transform in linearly correlated fuzzy space. Soft Comput 27, 1425–1438 (2023). https://doi.org/10.1007/s00500-022-07659-8

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