Existence of solution for fractional differential equations involving symmetric fuzzy numbers

Muhammad Sarwar; Noor Jamal; Kamaleldin Abodayeh; Manel Hleili; Thanin Sitthiwirattham; Chanon Promsakon; Muhammad Sarwar; Noor Jamal; Kamaleldin Abodayeh; Manel Hleili; Thanin Sitthiwirattham; Chanon Promsakon

doi:10.3934/math.2024717

AIMS Mathematics

2024, Volume 9, Issue 6: 14747-14764. doi: 10.3934/math.2024717

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Research article

Existence of solution for fractional differential equations involving symmetric fuzzy numbers

1.
Department of Mathematics, Univdersity of malakand, Dir Lower, Pakistan, sarwarswati@gmail.com, noorjamalmphil791@gmail.com
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia, kamal@psu.edu.sa
3.
Department of mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia, mhleili@ut.edu.sa
4.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand, thanin_sit@dusit.ac.th
5.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand, chanon.p@sci.kmutnb.ac.th
6.
Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand

Received: 28 February 2024 Revised: 06 April 2024 Accepted: 09 April 2024 Published: 23 April 2024
MSC : 35R13, 26E50, 34K37

Linear correlated fractional fuzzy differential equations (LCFFDEs) are one of the best tools for dealing with physical problems with uncertainty. The LCFFDEs mostly do not have unique solutions, especially if the basic fuzzy number is symmetric. The LCFFDEs of symmetric basic fuzzy numbers extend to the new system by extension and produce many solutions. The existing literature does not have any criteria to ensure the existence of unique solutions to LCFFDEs. In this study, we will explore the main causes of the extension and the unavailability of unique solutions. Next, we will discuss the existence and uniqueness conditions of LCFFDEs by using the concept of metric fixed point theory. For the useability of established results, we will also provide numerical examples and discuss their unique solutions. To show the authenticity of the solutions, we will also provide 2D and 3D plots of the solutions.
- fuzzy numbers,
- existence,
- uniqueness,
- symmetric fuzzy numbers,
- non-symmetric fuzzy numbers,
- uncertainty
Citation: Muhammad Sarwar, Noor Jamal, Kamaleldin Abodayeh, Manel Hleili, Thanin Sitthiwirattham, Chanon Promsakon. Existence of solution for fractional differential equations involving symmetric fuzzy numbers[J]. AIMS Mathematics, 2024, 9(6): 14747-14764. doi: 10.3934/math.2024717

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Abstract

Linear correlated fractional fuzzy differential equations (LCFFDEs) are one of the best tools for dealing with physical problems with uncertainty. The LCFFDEs mostly do not have unique solutions, especially if the basic fuzzy number is symmetric. The LCFFDEs of symmetric basic fuzzy numbers extend to the new system by extension and produce many solutions. The existing literature does not have any criteria to ensure the existence of unique solutions to LCFFDEs. In this study, we will explore the main causes of the extension and the unavailability of unique solutions. Next, we will discuss the existence and uniqueness conditions of LCFFDEs by using the concept of metric fixed point theory. For the useability of established results, we will also provide numerical examples and discuss their unique solutions. To show the authenticity of the solutions, we will also provide 2D and 3D plots of the solutions.

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