Qualitative behavior of a higher-order fuzzy difference equation

İbrahim Yalçınkaya; Durhasan Turgut Tollu; Alireza Khastan; Hijaz Ahmad; Thongchai Botmart; İbrahim Yalçınkaya; Durhasan Turgut Tollu; Alireza Khastan; Hijaz Ahmad; Thongchai Botmart

doi:10.3934/math.2023319

AIMS Mathematics

2023, Volume 8, Issue 3: 6309-6322. doi: 10.3934/math.2023319

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Research article

Qualitative behavior of a higher-order fuzzy difference equation

1.
Department of Mathematics and Computer Sciences, Necmettin Erbakan University, Konya 42090, Turkey
2.
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 3900186 Roma, Italy
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002 Thailand

Received: 24 January 2022 Revised: 15 May 2022 Accepted: 02 December 2022 Published: 03 January 2023
MSC : 39A10, 39A20, 39A26

In this paper, we investigate the qualitative behavior of the fuzzy difference equation

$ \begin{equation*} z_{n+1} = \frac{Az_{n-s}}{B+C\prod\limits_{i = 0}^{s}z_{n-i}} \end{equation*} $

where $ n\in \mathbb{N}_{0} = \; \mathbb{N} \cup \left\{ 0\right\}, \; (z_{n}) $ is a sequence of positive fuzzy numbers, $ A, B, C $ and the initial conditions $ z_{-j}, \; j = 0, 1, ..., s $ are positive fuzzy numbers and $ s $ is a positive integer. Moreover, two examples are given to verify the effectiveness of the results obtained.
- fuzzy difference equations,
- existence of positive solutions,
- boundedness,
- convergence
Citation: İbrahim Yalçınkaya, Durhasan Turgut Tollu, Alireza Khastan, Hijaz Ahmad, Thongchai Botmart. Qualitative behavior of a higher-order fuzzy difference equation[J]. AIMS Mathematics, 2023, 8(3): 6309-6322. doi: 10.3934/math.2023319

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Abstract

In this paper, we investigate the qualitative behavior of the fuzzy difference equation

$ \begin{equation*} z_{n+1} = \frac{Az_{n-s}}{B+C\prod\limits_{i = 0}^{s}z_{n-i}} \end{equation*} $

where $ n\in \mathbb{N}_{0} = \; \mathbb{N} \cup \left\{ 0\right\}, \; (z_{n}) $ is a sequence of positive fuzzy numbers, $ A, B, C $ and the initial conditions $ z_{-j}, \; j = 0, 1, ..., s $ are positive fuzzy numbers and $ s $ is a positive integer. Moreover, two examples are given to verify the effectiveness of the results obtained.

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