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Volume 14
Issue 12
10.3390/sym14122667
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Article

New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS

by
Zahra Eidinejad
1,
Reza Saadati
1,*,
Radko Mesiar
2,3,* and
Chenkuan Li
4
1
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
2
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
3
Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vodárenskou věží 4, 182 08 Praha, Czech Republic
4
Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada
*
Authors to whom correspondence should be addressed.
Symmetry 2022, 14(12), 2667; https://doi.org/10.3390/sym14122667
Submission received: 23 November 2022 / Revised: 2 December 2022 / Accepted: 10 December 2022 / Published: 16 December 2022
(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points)
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Abstract

By using a class of aggregation control functions, we introduce the concept of multiple-HU-OS1-stability and get an optimum approximation for a nonlinear single fractional differential equation (NS-ABC-FDE) with a Mittag–Leffler kernel. We apply an alternative fixed-point theorem to prove the existence of a unique solution and the multiple-HU-OS1-stability for the NS-ABC-FDE in the symmetric matrix-valued FBS. Finally, with an example, we show the application of the obtained results.
Keywords: stability analysis; aggregation function; control function; fractional differential equations; fuzzy sets; fixed point stability analysis; aggregation function; control function; fractional differential equations; fuzzy sets; fixed point

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MDPI and ACS Style

Eidinejad, Z.; Saadati, R.; Mesiar, R.; Li, C. New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS. Symmetry 2022, 14, 2667. https://doi.org/10.3390/sym14122667

AMA Style

Eidinejad Z, Saadati R, Mesiar R, Li C. New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS. Symmetry. 2022; 14(12):2667. https://doi.org/10.3390/sym14122667

Chicago/Turabian Style

Eidinejad, Zahra, Reza Saadati, Radko Mesiar, and Chenkuan Li. 2022. "New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS" Symmetry 14, no. 12: 2667. https://doi.org/10.3390/sym14122667

APA Style

Eidinejad, Z., Saadati, R., Mesiar, R., & Li, C. (2022). New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS. Symmetry, 14(12), 2667. https://doi.org/10.3390/sym14122667

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