Fractional Differentiation and Integration for Fuzzy Functions on Time Scales

Authors

  • Mina Shahidi
  • Estevão Esmi
  • Laécio Carvalho de Barros

DOI:

https://doi.org/10.5540/03.2023.010.01.0056

Keywords:

Time Scales, Fuzzy Functions, Fuzzy Fractional Derivative, Fuzzy Fractional Integral

Abstract

In this paper, we propose a new definition of the fractional derivative and fractional integral for fuzzy functions on time scales. The introduced derivative is a natural extension of the Hukuhara derivative. Furthermore, some properties of the introduced derivative and integral are studied. Some examples are provided to illustrate the obtained results.

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Author Biographies

Mina Shahidi

Department of Applied Mathematics, University of Campinas

Estevão Esmi

Department of Applied Mathematics, University of Campinas

Laécio Carvalho de Barros

Department of Applied Mathematics, University of Campinas

References

B. Bede. Mathematics of Fuzzy Sets and Fuzzy Logic. 2013.

N. Benkhettou, A. M. B. da Cruz, and D.F.M Torres. “A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration”. In: Signal Processing 107 (2015), pp. 230–237.

M. Bohner and A. Peterson. Dynamic equations on time scales: An introduction with applications. Springer Science & Business Media, 2001.

M. Caputo and C. Cametti. “Diffusion with memory in two cases of biological interest”. In: Journal of Theoretical Biology 254 (2008), pp. 697–703.

M. Caputo and M. Fabrizio. “Damage and fatigue described by a fractional derivative model”. In: Journal of Computational Physics 293 (2015), pp. 400–408.

O. S. Fard and T. A. Bidgoli. “Calculus of fuzzy functions on time scales (I)”. In: Soft Computing 19 (2015), pp. 293–305.

S. Hilger. “Analysis on measure chains-a unified approach to continuous and discrete calculus”. In: Results in Mathematics 18 (1990), pp. 18–56.

A. Khastan and R. Rodrıguez-López. “On the solutions to first order linear fuzzy differential equations”. In: Fuzzy Sets and Systems 295 (2016), pp. 114–135.

K. Oldham and J. Spanier. The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier, 1974.

M. Shahidi and A. Khastan. “New Fractional Derivative for Fuzzy Functions and Its Applications on Time Scale”. In: Nonlinear Dynamics and Complexity: Mathematical Modelling of Real-World Problems. Springer, 2022, pp. 337–354.

C. Vasavi, G. S. Kumar, and M. S. N. Murty. “Generalized differentiability and integrability for fuzzy set-valued functions on time scales”. In: Soft Computing 20 (2016), pp. 1093–1104.

L. A. Zadeh. “Fuzzy sets”. In: Information and Control 8 (1965), pp. 338–353.

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Published

2023-12-18

Issue

Section

Trabalhos Completos