Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function

Abstract

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.

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

“…We also recall here some results obtained by applying fractional integral on different hypergeometric functions seen in papers [5][6][7]. Another interesting study of confluent (or Kummer) hypergeometric function was made in [8], which extended the study made in [9]. The univalence of confluent Kummer function was also studied in [10].…”

“…The univalence of confluent Kummer function was also studied in [10]. Inspired by the study from [8], we present here a new fractional integral operator connecting two other important operators, namely the Atangana-Baleanu integral operator and Riemann-Liouville.…”

Some Subordination Results for Atangana-Baleanu Fractional Integral Operator Involving Bessel Functions

“…By means of certain fractional integral operators, in papers [8,9], some inequalities and properties concerning a subclass of analytic functions are derived. Very recently, the paper [10] was published concerning a confluent (or Kummer) hypergeometric function. This study extends a result obtained in [11].…”

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

“…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.…”