Ibrahim, Rabha W.Baleanu, DumitruBaleanu, DumitruMatematik2024-04-252024-04-252022Ibrahim, Rabha W.; Baleanu, Dumitru. (2022). "Modified Atangana-Baleanu Fractional Differential Operators", Proceedings of the Institute of Mathematics and Mechanics, Vol.48, No.SI, pp.56-67.2409-49862409-4994https://doi.org/10.30546/2409-4994.48.2022.5667Fractional differential operators are mostly investigated for functions of real variables. In this paper, we present two fractional differential operators for a class of normalized analytic functions in the open unit disk. The suggested operators are investigated according to concepts in geometric function theory, using the concepts of convexity and starlikeness. Therefore, we reformulate the new operators in the Ma-Minda class of analytic functions, in order to act on normalized analytic functions. Our method is based on subordination, superordination, and majorization theory. As an application, we employ these operators to generalize Bernoulli's equation and a special class of Briot-Bouquet equations. The solution of the generalized equation is formulated by a hypergeometric function.eninfo:eu-repo/semantics/closedAccessSubordination And SuperordinationUnivalent FunctionAnalytic FunctionOpen Unit DiskSpecial FunctionFractional CalculusFractional Differential OperatorArticle48Special Issue566710.30546/2409-4994.48.2022.56672-s2.0-85142630835WOS:000931992300004N/AQ2