Abstract
The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. The original theorems proved in the paper generate interesting corollaries for particular choices of functions acting as fuzzy best dominant and fuzzy best subordinant. Another contribution contained in this paper is the nice sandwich-type theorem combining the results given in two theorems proved here using the two theories of fuzzy differential subordination and fuzzy differential superordination.
Highlights
The concept of fuzzy differential subordination and its dual, the concept of fuzzy differential superordination were introduced in the last decade as a result of the trend for adapting the notion of fuzzy set to different topics of research
Following the research line in which fuzzy differential subordinations and superordinations are connected to operators, the interesting fractional integral of confluent hypergeometric function introduced and investigated in [36] using the classical theories of differential subordinations and superordinations is further considered from this new perspective involving fuzzy set theory notions
The interesting operator presented in Definition 3 was previously defined and studied related to several aspects of differential subordination theory in [36] as a fractional integral of confluent hypergeometric function
Summary
The concept of fuzzy differential subordination and its dual, the concept of fuzzy differential superordination were introduced in the last decade as a result of the trend for adapting the notion of fuzzy set to different topics of research. Applications of differential subordination theory to analytic and p-valent functions defined by a generalized fractional differintegral operator were presented in [34] and a new fractional integral operator is used in the study on the Mittag–Leffler-confluent hypergeometric function [35]. Following the research line in which fuzzy differential subordinations and superordinations are connected to operators, the interesting fractional integral of confluent hypergeometric function introduced and investigated in [36] using the classical theories of differential subordinations and superordinations is further considered from this new perspective involving fuzzy set theory notions. The purpose of the investigation is to present new fuzzy differential subordinations and superordinations which lead to interesting corollaries when using functions with remarkable geometric properties known from geometric function theory as fuzzy best dominant and fuzzy best subordinant, respectively
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