Fractional Integral of the Confluent Hypergeometric Function Related to Fuzzy Differential Subordination Theory

Abstract

The fuzzy differential subordination concept was introduced in 2011, generalizing the concept of differential subordination following a recent trend of adapting fuzzy sets theory to other already-established theories. A prolific tool in obtaining new results related to operators is the fractional integral applied to different functions. The fractional integral of the confluent hypergeometric function was previously investigated using means of the classical theory of subordination. In this paper, we give new applications of this function using the theory of fuzzy differential subordination. Fuzzy differential subordinations are established and their best dominants are also provided. Corollaries are written using particular functions, in which the conditions for the univalence of the fractional integral of the confluent hypergeometric function are given. An example is constructed as a specific application of the results obtained in this paper.

Keywords

• fuzzy set
• univalent function
• fuzzy differential subordination
• fuzzy best dominant
• confluent hypergeometric function
• fractional integral of order α