{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:26:56Z","timestamp":1760236016097,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T00:00:00Z","timestamp":1634169600000},"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>The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana\u2013Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.<\/jats:p>","DOI":"10.3390\/sym13101929","type":"journal-article","created":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T23:02:16Z","timestamp":1634252536000},"page":"1929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Fuzzy Differential Subordination of the Atangana\u2013Baleanu Fractional Integral"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2855-7535","authenticated-orcid":false,"given":"Alina","family":"Alb Lupa\u015f","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1000-7375","authenticated-orcid":false,"given":"Adriana","family":"C\u0103ta\u015f","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,14]]},"reference":[{"key":"ref_1","first-page":"97","article-title":"The notion of subordination in fuzzy sets theory","volume":"19","author":"Oros","year":"2011","journal-title":"Gen. Math."},{"key":"ref_2","first-page":"55","article-title":"Fuzzy differential subordination","volume":"3","author":"Oros","year":"2012","journal-title":"Acta Univ. Apulensis"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations. Theory and Applications, Marcel Dekker, Inc.","DOI":"10.1201\/9781482289817"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"129","DOI":"10.34198\/ejms.4120.129137","article-title":"Fuzzy Differential Subordinations Results for \u03bb-pseudo Starlike and \u03bb-pseudo Convex Functions with Respect to Symmetrical Points","volume":"4","author":"Wanas","year":"2020","journal-title":"Earthline J. Math. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"229","DOI":"10.31801\/cfsuasmas.784080","article-title":"New fuzzy differential subordinations","volume":"70","author":"Oros","year":"2021","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Srivastava, H.M., and El-Deeb, S.M. (2021). Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution. Symmetry, 13.","DOI":"10.3390\/sym13061023"},{"key":"ref_8","first-page":"51","article-title":"Some properties for fuzzy differential subordination defined by Wanas operator","volume":"4","author":"Wanas","year":"2020","journal-title":"Earthline J. Math. Sci."},{"key":"ref_9","first-page":"133","article-title":"Fuzzy differential subordinations associated with an integral operator","volume":"XXVII","year":"2020","journal-title":"An. Univ. Oradea Fasc. Mat."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Alb Lupa\u015f, A., and Oros, G.I. (2021). New Applications of S\u0103l\u0103gean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations. Mathematics, 9.","DOI":"10.3390\/math9162000"},{"key":"ref_11","unstructured":"El-Deeb, S.M., and Oros, G.I. (2021). Fuzzy differential subordinations connected with the linear operator. Math. Bohem., 1\u201310."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1186\/s13662-021-03393-x","article-title":"On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: A new fractional analysis and control","volume":"2021","author":"Baleanu","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1186\/s13662-021-03320-0","article-title":"Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system","volume":"2021","author":"Baleanu","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_14","first-page":"105","article-title":"The fractional dynamics of a linear triatomic molecule","volume":"73","author":"Baleanu","year":"2021","journal-title":"Rom. Rep. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1186\/s13662-021-03454-1","article-title":"A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system","volume":"2021","author":"Baleanu","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"12114","DOI":"10.3934\/math.2021703","article-title":"Initial boundary value problems for a multi-term time fractional diffusion equation with generalized fractional derivatives in time","volume":"6","author":"Zhou","year":"2021","journal-title":"AIMS Math."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Rashid, S., Khalid, A., Bazighifan, O., and Oros, G.I. (2021). New modifications of integral inequalities via \u03b3-convexity pertaining to fractional calculus and their applications. Mathematics, 9.","DOI":"10.3390\/math9151753"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3605","DOI":"10.1002\/mma.6966","article-title":"An analytical study on Mittag-Leffler-confluent hypergeometric functions with fractional integral operator","volume":"44","author":"Ghanim","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ghanim, F., Al-Janaby, H., and Bazighifan, O. (2021). Some New Extensions on Fractional Differential and Integral Properties for Mittag-Leffler Confluent Hypergeometric Function. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5040143"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rashid, S., Ashraf, R., Akdemir, A.O., Alqudah, M.A., Abdeljawad, T., and Mohamed, M.S. (2021). Analytic Fuzzy Formulation of a Time-Fractional Fornberg\u2013Whitham Model with Power and Mittag\u2013Leffler Kernels. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5030113"},{"key":"ref_21","first-page":"10","article-title":"Fuzzy subordination results for fractional integral associated with generalized Mittag-Leffler function","volume":"2019","author":"Wanas","year":"2019","journal-title":"Eng. Math. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"27","DOI":"10.29304\/jqcm.2020.12.3.708","article-title":"Some Results for Fractional Derivative Associated with Fuzzy Differential Subordinations","volume":"12","author":"Wanas","year":"2020","journal-title":"J. Al-Qadisiyah Comput. Sci. Math."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Alb Lupa\u015f, A., and C\u0103ta\u015f, A. (2021). An Application of the Principle of Differential Subordination to Analytic Functions Involving Atangana-Baleanu Fractional Integral of Bessel Functions. Symmetry, 13.","DOI":"10.3390\/sym13060971"},{"key":"ref_24","unstructured":"Gal, S.G., and Ban, A.I. (1996). Elemente de Matematic\u0103 Fuzzy, University of Oradea."},{"key":"ref_25","first-page":"239","article-title":"Dominants and best dominants in fuzzy differential subordinations","volume":"57","author":"Oros","year":"2012","journal-title":"Stud. Univ. Babe\u015f-Bolyai Math."},{"key":"ref_26","unstructured":"Samko, S.G., Kilbas, A.A., and Marichev, O.I. (2002). Fractional Integrals and Derivatives: Theory and Applications, Taylor & Francis."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8070","DOI":"10.1002\/mma.5754","article-title":"A complex analysis approach to Atangana-Baleanu fractional calculus","volume":"44","author":"Fernandez","year":"2019","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"155","DOI":"10.5486\/PMD.2008.4126","article-title":"Geometric properties of generalized Bessel functions","volume":"73","author":"Baricz","year":"2008","journal-title":"Publ. Math. Debr."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Baricz, \u00c1. (2010). Geometric properties of generalized Bessel functions. Generalized Bessel Functions of the First Kind, Springer.","DOI":"10.1007\/978-3-642-12230-9"},{"key":"ref_30","first-page":"27","article-title":"Fuzzy Differential Superordination","volume":"7","author":"Atshan","year":"2017","journal-title":"Theory Appl. Math. Comput. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1929\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:12:56Z","timestamp":1760166776000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,14]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101929"],"URL":"https:\/\/doi.org\/10.3390\/sym13101929","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,14]]}}}