Abstract
In thispaper, we present a brief study on the fractional derivative of Caputo in the space of linearly correlated fuzzy numbers (\(\mathbb {R}_{\mathcal {F}(A)}\)), with a non-symmetric fuzzy number A. This space is interesting since it has a Banach space structure. The use of the Caputo derivative gives the advantage of including memory effect in the dynamics of mathematical models, allowing a better description of real phenomena. To illustrate the proposed concepts, we study the curve of cumulative cases of COVID-19 in China through a fractional logistic model in space \(\mathbb {R}_{\mathcal {F}(A)}\).
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Acknowledgements
This study was partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, by the Brazilian National Council for Scientific and Technological Development (CNPq), under grants 313313/2020-2 and 314885/2021-8, and by FAPESP under grant 2020/09838-0.
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Lopes, M.M., Pedro, F.S., Laiate, B., Esmi, E., Barros, L.C. (2023). A Note on Caputo Fractional Derivative in the Space of Linearly Correlated Fuzzy Numbers. In: Dick, S., Kreinovich, V., Lingras, P. (eds) Applications of Fuzzy Techniques. NAFIPS 2022. Lecture Notes in Networks and Systems, vol 500. Springer, Cham. https://doi.org/10.1007/978-3-031-16038-7_13
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