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New Fractional Derivative for Fuzzy Functions and Its Applications on Time Scale

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Nonlinear Dynamics and Complexity

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 36))

Abstract

We propose a new definition of fractional derivative and fractional integral for fuzzy functions on time scales. Also, some properties of the introduced derivative and integral are studied. Furthermore, we provide sufficient conditions for the fractional derivative to preserve the addition and the scalar multiplication. Moreover, we study fuzzy fractional differential equations using the concept of fractional differentiability on time scales and present the general form of their solutions. Some examples are provided to illustrate the results, as well.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran

    Mina Shahidi & Alireza Khastan

Authors
  1. Mina Shahidi
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  2. Alireza Khastan
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Corresponding author

Correspondence to Mina Shahidi .

Editor information

Editors and Affiliations

  1. School of Engineering, Polytechnic Institute of Porto, Porto, Portugal

    Carla M.A. Pinto

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Shahidi, M., Khastan, A. (2022). New Fractional Derivative for Fuzzy Functions and Its Applications on Time Scale. In: Pinto, C.M. (eds) Nonlinear Dynamics and Complexity. Nonlinear Systems and Complexity, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-06632-0_16

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