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On the existence of approximate solutions to fuzzy delay differential equations under the metric derivative

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Abstract

In this paper, we use a metric derivative which is based on the Hausdorff distance between fuzzy numbers. Using this concept of differentiability, we study fuzzy delay differential equations and also prove a result which guarantees the existence of the approximate solutions. The proof of this result is constructive and provides a method to obtain approximate solutions based on fuzzy arithmetic. In order to illustrate the applicability of the presented results, we provide an example with Hutchinson equation and other with a two-dimensional system.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable suggestions. This article was partially supported by Fapesp under grants no. 2022/00196-1 and 2020/09838-0 and by CNPq under grant no. 313313/2020-2.

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  1. Department of Mathematics, Statistic and Scientific Computing, Unicamp, Campinas, Brazil

    M. Shahidi & E. Esmi

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  1. M. Shahidi
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  2. E. Esmi
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Correspondence to M. Shahidi.

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Communicated by Leonardo Tomazeli Duarte.

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Shahidi, M., Esmi, E. On the existence of approximate solutions to fuzzy delay differential equations under the metric derivative. Comp. Appl. Math. 41, 412 (2022). https://doi.org/10.1007/s40314-022-02132-6

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  • DOI: https://doi.org/10.1007/s40314-022-02132-6

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