{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:43:09Z","timestamp":1760402589759,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A class of Briot\u2013Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot\u2013Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.<\/jats:p>","DOI":"10.3390\/axioms9020042","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T04:49:38Z","timestamp":1587444578000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9341-025X","authenticated-orcid":false,"given":"Rabha W.","family":"Ibrahim","sequence":"first","affiliation":[{"name":"Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Mathematics &amp; Statistics, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4267-310X","authenticated-orcid":false,"given":"Rafida M.","family":"Elobaid","sequence":"additional","affiliation":[{"name":"Department of General Sciences, Prince Sultan University, Riyadh 12435, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4523-2385","authenticated-orcid":false,"given":"Suzan J.","family":"Obaiys","sequence":"additional","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya 62200, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,21]]},"reference":[{"key":"ref_1","first-page":"781","article-title":"On special differential subordinations using Salagean and Ruscheweyh operators","volume":"12","author":"Lupas","year":"2009","journal-title":"Math. Inequal. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1090\/S0002-9939-1975-0367176-1","article-title":"New criteria for univalent functions","volume":"49","author":"Ruscheweyh","year":"1975","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/BFb0066543","article-title":"Subclasses of univalent functions","volume":"Volume 1013","author":"Salagean","year":"1983","journal-title":"Complex Analysis\u2014Fifth Romanian-Finnish Seminar"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.matcom.2020.02.016","article-title":"Arched foot based on conformal complex neural network testing","volume":"174","author":"Ibrahim","year":"2020","journal-title":"Math. Comput. Simul."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1016\/j.jksus.2020.02.024","article-title":"Conformal Geometry of the Turtle Shell","volume":"32","author":"Ibrahim","year":"2020","journal-title":"J. King Saud Univ. Sci."},{"key":"ref_6","first-page":"573","article-title":"Subordination inequalities of a new Salagean-difference operator","volume":"14","author":"Ibrahim","year":"2019","journal-title":"Int. J. Math. Comput. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1989-0951883-8","article-title":"Differential-difference operators associated with reflections groups","volume":"311","author":"Dunkl","year":"1989","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1016\/j.physleta.2015.01.023","article-title":"The Dunkl-Coulomb problem in the plane","volume":"379","author":"Genest","year":"2015","journal-title":"Phys. Lett. A"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Koelink, E., and Van Assche, W. (2003). Dunkl Operators: Theory and Applications. Orthogonal Polynomials and Special Functions, Springer.","DOI":"10.1007\/b12166"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations: Theory and Applications, CRC Press.","DOI":"10.1201\/9781482289817"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ebrahimi, F., Mohammadi, K., Barouti, M.M., and Habibi, M. (2019). Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell. Waves Random Complex Media, 1\u201327.","DOI":"10.1080\/17455030.2019.1694729"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s40430-019-1715-x","article-title":"Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell","volume":"41","author":"Habibi","year":"2019","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ibrahim, R.W., Hadid, S.B., and Momani, S. (2020). Generalized Briot\u2013Bouquet differential equation by a quantum difference operator in a complex domain. Int. J. Dyn. Control, 1\u201310.","DOI":"10.2478\/gm-2020-0008"},{"key":"ref_14","unstructured":"Ma, W.C., and Minda, D. (1992, January 19\u201323). A unified treatment of some special classes of univalent functions. Proceedings of the Conference on Complex Analysis, Tianjin, China."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s41980-018-0127-5","article-title":"Radius problems for starlike functions associated with the sine function","volume":"45","author":"Cho","year":"2019","journal-title":"Bull. Iran. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s13398-017-0466-8","article-title":"Starlike functions associated with exponential function and the lemniscate of Bernoulli","volume":"113","author":"Khatter","year":"2019","journal-title":"Rev. Real Acad. Cienc. Exactas Ser. A Mat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s40840-014-0026-8","article-title":"On a subclass of strongly starlike functions associated with exponential function","volume":"38","author":"Mendiratta","year":"2015","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1515\/ms-2017-0289","article-title":"Sharp coefficient bounds for starlike functions associated with the Bell numbers","volume":"69","author":"Kumar","year":"2019","journal-title":"Math. Slovaca"},{"key":"ref_19","first-page":"647","article-title":"Conic domains and starlike functions","volume":"45","author":"Kanas","year":"2000","journal-title":"Rev. Roum. Math. Pures Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.5556\/j.tkjm.25.1994.4448","article-title":"Univalent functions with positive coefficients","volume":"25","author":"Uralegaddi","year":"1994","journal-title":"Tamkang J. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1186\/1687-1847-2013-150","article-title":"Some differential subordinations using Ruscheweyh derivative and Salaagean operator","volume":"2013","year":"2013","journal-title":"Adv. Differ. Equ."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yousef, A.T., and Salleh, Z. (2020). On a Harmonic Univalent Subclass of Functions Involving a Generalized Linear Operator. 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