Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces

Noor Jamal; Muhammad Sarwar; Nabil Mlaiki; Ahmad Aloqaily; Noor Jamal; Muhammad Sarwar; Nabil Mlaiki; Ahmad Aloqaily

doi:10.3934/math.2024134

AIMS Mathematics

2024, Volume 9, Issue 2: 2695-2721. doi: 10.3934/math.2024134

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Research article

Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces

1.
Department of Mathematics, University of Malakand, Dir Lower, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia

Received: 22 November 2023 Revised: 04 December 2023 Accepted: 07 December 2023 Published: 28 December 2023
MSC : 26E50, 35R13

Linear correlated fuzzy differential equations (LCFDEs) are a valuable approach to handling physical problems, optimizations problems, linear programming problems etc. with uncertainty. But, LCFDEs employed on spaces with symmetric basic fuzzy numbers often exhibit multiple solutions due to the extension process. This abundance of solutions poses challenges in the existing literature's solution methods for LCFDEs. These limitations have led to reduced applicability of LCFDEs in dealing with such types of problems. Therefore, in the current study, we focus on establishing existence and uniqueness results for LCFDEs. Moreover, we will discuss solutions in the canonical form of LCFDEs in the space of symmetric basic fuzzy number which is currently absent in the literature. To enhance the practicality of our work, we provide examples and plots to illustrate our findings.
- Non-increasing diameter,
- non-decreasing diameter,
- extend system,
- uncertainty,
- nodal point,
- symmetric and non-symmetric numbers,
- linear correlation,
- nodal point
Citation: Noor Jamal, Muhammad Sarwar, Nabil Mlaiki, Ahmad Aloqaily. Solution of linear correlated fuzzy differential equations in the linear correlated fuzzy spaces[J]. AIMS Mathematics, 2024, 9(2): 2695-2721. doi: 10.3934/math.2024134

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Abstract

Linear correlated fuzzy differential equations (LCFDEs) are a valuable approach to handling physical problems, optimizations problems, linear programming problems etc. with uncertainty. But, LCFDEs employed on spaces with symmetric basic fuzzy numbers often exhibit multiple solutions due to the extension process. This abundance of solutions poses challenges in the existing literature's solution methods for LCFDEs. These limitations have led to reduced applicability of LCFDEs in dealing with such types of problems. Therefore, in the current study, we focus on establishing existence and uniqueness results for LCFDEs. Moreover, we will discuss solutions in the canonical form of LCFDEs in the space of symmetric basic fuzzy number which is currently absent in the literature. To enhance the practicality of our work, we provide examples and plots to illustrate our findings.

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