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Research Article | Open Access

Qualitative behavior of a higher-order fuzzy difference equation

İbrahim Yalçınkaya1, Durhasan Turgut Tollu1, Alireza Khastan2, Hijaz Ahmad3, Thongchai Botmart4( )
Department of Mathematics and Computer Sciences, Necmettin Erbakan University, Konya 42090, Turkey
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
​Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 3900186 Roma, Italy
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002 Thailand
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Abstract

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

z n + 1 = A z n − s B + C ∏ i = 0 s z n − i

where n ∈ N 0 = N ∪ { 0 } , ( 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.

Keywords

fuzzy difference equationsexistence of positive solutionsboundednessconvergence
CLC number: 39A10, 39A20, 39A26

References

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 6309-6322
DOI: 10.3934/math.2023319

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Yalçınkaya İ, Tollu DT, Khastan A, et al. Qualitative behavior of a higher-order fuzzy difference equation. AIMS Mathematics, 2023, 8(3): 6309-6322. https://doi.org/10.3934/math.2023319

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Received: 24 January 2022
Revised: 15 May 2022
Accepted: 02 December 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)