Properties of a Subclass of Analytic Functions Defined by Using an Atangana–Baleanu Fractional Integral Operator

Abstract

The Atangana–Baleanu fractional integral and multiplier transformations are two functions successfully used separately in many recently published studies. They were previously combined and the resulting function was applied for obtaining interesting new results concerning the theories of differential subordination and fuzzy differential subordination. In the present investigation, a new approach is taken by using the operator previously introduced by applying the Atangana–Baleanu fractional integral to a multiplier transformation for introducing a new subclass of analytic functions. Using the methods familiar to geometric function theory, certain geometrical properties of the newly introduced class are obtained such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity, and close-to-convexity of functions belonging to the class. This class may have symmetric or assymetric properties. The results could prove interesting for future studies due to the new applications of the operator and because the univalence properties of the new subclass of functions could inspire further investigations having it as the main focus.

New Applications of the Fractional Integral on Analytic Functions

“…Many papers, such as [1,2], studied different operators defined by using the fractional integral of order λ also used earlier by S. Owa [3]. Despite that, we also refer to [4][5][6] for theoretical and numerical analyses from real models described by classical PDEs and related operators.…”