Novel Results on Applications of Differential Subordination on Analytic Functions Associated with Zeta-Riemann Fractional Differential Operator

Abstract

The findings of this study are connected with geometric function theory and are obtained by using subordination-based techniques in conjunction with Zeta-Riemann fractional differential operator information. We used the Zeta-Riemann fractional differential operator to investigate a certain classes of analytic functions. It is shown that, for particular choice of parameters for the new generalized classes, the classes of starlike, close-to-convex and α-convex functions emerges. Many classes of univalent functions are studied using convolution and subordination principle. Furthermore, some classes are defined and developed by using the Zeta-Riemann fractional differential operator. The connections between the classes are presented in the definitions and associated remarks, and characterization properties are also proved, including combinations of functions belonging to those classes and inclusion relations.