Ibrahim, Rabha W.Salahshour, SoheilPall-szabo, Agnes Orsolya2024-10-152024-10-15202402075-168010.3390/axioms13080522https://doi.org/10.3390/axioms13080522https://hdl.handle.net/20.500.14517/6587Salahshour, Soheil/0000-0003-1390-3551; Agnes Orsolya, Pall-Szabo/0000-0003-3469-3362; Ibrahim, Rabha W./0000-0001-9341-025XBy using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal-fractional differential and integral operators of a complex variable in an open unit disk are defined and investigated analytically and geometrically. We address some inequalities involving the generalized fractal-fractional integral operator in some spaces of analytic functions. A novel complex fractal-fractional integral transform (CFFIT) is presented. A normalization of the proposed CFFIT is observed in the open unit disk. Examples are illustrated for power series of analytic functions.eninfo:eu-repo/semantics/openAccessfractional calculusfractal calculusfractional difference operatorfractal-fractional differential operatorfractal-fractional calculuscomplex transformsubordination and superordinationArticleQ2138WOS:001305164200001