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On the dynamics of a higher-order fuzzy difference equation with rational terms

  • Fuzzy systems and their mathematics
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Abstract

In this paper, we investigate existence, boundedness, asymptotic behavior and the oscillatory behavior of the positive solutions of the fuzzy difference equation

$$\begin{aligned} z_{n+1}=A+\frac{B}{z_{n-m_{1}}}+\frac{C}{z_{n-m_{2}}},\quad n\in \mathbb {N} _{0}, \end{aligned}$$

where \((z_{n})\) is a sequence of positive fuzzy numbers, A, B, C and the initial values \(z_{-j},\) \(j=0,1,\ldots ,s\), are positive fuzzy numbers and \( m_{1},m_{2}\) are nonnegative integers with \(s=\max \left\{ m_{1},m_{2}\right\} \). By studying this equation, we generalize and improve some results from the literature.

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No funding was received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090, Konya, Turkey

    İbrahim Yalçınkaya & Durhasan Turgut Tollu

  2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Hamdy El-Metwally

  3. Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Biruni University, Istanbul, Turkey

    Mustafa Bayram

Authors
  1. İbrahim Yalçınkaya
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  2. Hamdy El-Metwally
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  3. Mustafa Bayram
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  4. Durhasan Turgut Tollu
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All authors equally contributed to the study.

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Correspondence to Mustafa Bayram.

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Yalçınkaya, İ., El-Metwally, H., Bayram, M. et al. On the dynamics of a higher-order fuzzy difference equation with rational terms. Soft Comput 27, 10469–10479 (2023). https://doi.org/10.1007/s00500-023-08586-y

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