Ibrahim, Rabha W.Baleanu, DumitruBaleanu, DumitruMatematik2022-11-102022-11-102021Ibrahim, Rabha W.; Baleanu, Dumitru (2021). "On quantum hybrid fractional conformable differential and integral operators in a complex domain", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol. 115, No. 1.1578-73031579-1505https://doi.org/10.1007/s13398-020-00982-5Ibrahim, Rabha W./0000-0001-9341-025XNewly, the hybrid fractional differential operator (HFDO) is presented and studied in Baleanu et al. (Mathematics 8.3:360, 2020). This work deals with the extension of HFDO to the complex domain and its generalization by using the quantum calculus. The outcome of the above conclusion is a q-HFDO, which will employ to introduce some classes of normalized analytic functions containing the well-known starlike and convex classes. Moreover, we utilize the quantum calculus to formulate the q-integral operator corresponding to q-HFDO. As a result, the upper solution is exemplified by utilizing the notion of subordination inequality.eninfo:eu-repo/semantics/closedAccessConformable CalculusDifferential OperatorUnivalent FunctionAnalytic FunctionSubordination And SuperordinationUnit DiskFractional CalculusQuantum Calculus30C5530C45Article115110.1007/s13398-020-00982-52-s2.0-85098483702WOS:000606398800001Q1Q1