{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:38:05Z","timestamp":1760233085895,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T00:00:00Z","timestamp":1671148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2013Leffler 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.<\/jats:p>","DOI":"10.3390\/sym14122667","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T06:58:29Z","timestamp":1671433109000},"page":"2667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2517-3365","authenticated-orcid":false,"given":"Zahra","family":"Eidinejad","sequence":"first","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6770-6951","authenticated-orcid":false,"given":"Reza","family":"Saadati","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6503-949X","authenticated-orcid":false,"given":"Radko","family":"Mesiar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinsk\u00e9ho 11, 810 05 Bratislava, Slovakia"},{"name":"Institute of Information Theory and Automation, The Czech Academy of Sciences, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 4, 182 08 Praha, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7098-8059","authenticated-orcid":false,"given":"Chenkuan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.chaos.2018.10.006","article-title":"On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative","volume":"117","author":"Jarad","year":"2018","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.chaos.2018.10.007","article-title":"Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana-Baleanu fractional operator","volume":"117","author":"Arqub","year":"2018","journal-title":"Chaos Solitons Fractals"},{"key":"ref_3","first-page":"2740678","article-title":"Generalized Euler-Lagrange equations for fuzzy fractional variational problems under gH-Atangana-Baleanu differentiability","volume":"2018","author":"Zhang","year":"2018","journal-title":"J. Funct. Spaces"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1186\/s13662-016-0949-5","article-title":"Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels","volume":"2016","author":"Abdeljawad","year":"2016","journal-title":"Adv. Differ. Eq."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0034-4877(17)30059-9","article-title":"On fractional derivatives with exponential kernel and their discrete versions","volume":"80","author":"Abdeljawad","year":"2017","journal-title":"Rep. Math. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Eidinejad, Z., Saadati, R., and de la Sen, M. (2021). Radu-Mihet Method for the Existence, Uniqueness, and Approximation of the \u03c8-Hilfer Fractional Equations by Matrix-Valued Fuzzy Controllers. Axioms, 10.","DOI":"10.3390\/axioms10020063"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Eidinejad, Z., Saadati, R., and Mesiar, R. (2022). 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Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics, Springer International Publishing.","DOI":"10.1007\/978-3-030-22591-9"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1186\/s13662-018-1594-y","article-title":"Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives","volume":"2018","author":"Gambo","year":"2018","journal-title":"Adv. Differ. 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