An Application of the Principle of Differential Subordination to Analytic Functions Involving Atangana–Baleanu Fractional Integral of Bessel Functions

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The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

“…The operator that will be used for the research presented in the original part of this paper was introduced in [23] and studied using the classical theory of differential subordination. In this paper, the study is extended and uses the notion of fuzzy differential subordination.…”

Section: Definition 2 ([1]mentioning

confidence: 99%

Fuzzy Differential Subordination of the Atangana–Baleanu Fractional Integral

Lupaş¹,

Cătaş²

2021

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“…Fractional integral was used intensely for obtaining new operators which have generated interesting subclasses of functions providing useful and inspiring outcome related to them [16][17][18][19][20][21]. Similar methods are used in the present investigation for obtaining the original results shown in the next section.…”

Section: Introductionmentioning

confidence: 96%

On Special Differential Subordinations Using Fractional Integral of Sălăgean and Ruscheweyh Operators

Lupaş

Oros

2021

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In the present paper, a new operator denoted by Dz−λLαn is defined by using the fractional integral of Sălăgean and Ruscheweyh operators. By means of the newly obtained operator, the subclass Snδ,α,λ of analytic functions in the unit disc is introduced, and various properties and characteristics of this class are derived by applying techniques specific to the differential subordination concept. By studying the operator Dz−λLαn, some interesting differential subordinations are also given.

“…Owa [6] and Owa and Srivastava [7] applied fractional integral calculus for a function that gives new possibilities in studying the function's properties. Atangana and Baleanu [8] generalized the fractional integral, which was studied by many researchers [9][10][11][12][13]. The fractional integral was investigated in its relation to Mittag-Leffler functions by many authors (see for example [14][15][16]), connected to Bessel functions and to different operators [17].…”

Section: Introductionmentioning

confidence: 99%

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

Lupaş

Cătaş

2022

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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.