Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations

Abstract

Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractional integral of Gaussian hypergeometric function is defined in this paper and using properties of the subordination chains, new fuzzy differential subordinations are obtained. Dominants of the fuzzy differential subordinations are given and using particular functions as such dominants, interesting geometric properties interpreted as inclusion relations of certain subsets of the complex plane are presented in the corollaries of the original theorems stated. An example is constructed as an application of the newly proved results.