**4. Conclusions**

Since the study of operators using the fuzzy differential subordination theory presents interest at this time, and many new and interesting results have been obtained recently, the research regarding this topic is further conducted in this paper. A new hypergeometric integral operator *<sup>M</sup>*(*z*) is introduced in this paper in relation (7) by using a confluent (or Kummer) hypergeometric function and, having as inspiration, the operator studied by Miller, Mocanu and Reade in 1978 [28] and taking specific values for parameters *β*, *γ*, *α*, *δ*

involved in its definition. Using the notion of fuzzy differential subordination and results related to it, in the first theorem proved, the fuzzy best dominant of a certain fuzzy differential subordination is given. Using particular functions as fuzzy best dominants, several corollaries are stated, giving sufficient conditions for the operator *<sup>M</sup>*(*z*) to be starlike, convex, starlike of order 1 2 and convex of order (−<sup>1</sup> 2 ), respectively. The second theorem proved shows the property of the operator *<sup>M</sup>*(*z*) to be close-to-convex. For further study, the properties already proved, related to starlikeness and convexity of the operator *<sup>M</sup>*(*z*), could inspire applications in introducing special classes of analytic functions. The operator could also be studied using the dual theory of fuzzy differential superordination, possibly obtaining sandwhich-type theorems, connecting with the present results a usual outcome in geometric function theory. Since particular values for parameters have been used for defining this operator, it might be interesting to try using other values for obtaining certain potentially interesting operators. It being well-known how hypergeometric functions have numerous applications in physics, engineering and statistics, applications of the operators involving those functions could prove useful in other disciplines. The theory of fuzzy differential subordination is still very new and one cannot predict what applications in real life or other scientific domains it might have. Those are subjects for investigation in long-term future studies.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.
