New Applications of the Fractional Integral on Analytic Functions

Abstract

The fractional integral is a function known for the elegant results obtained when introducing new operators; it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories.

Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

“…The fractional integral has been extensively exploited to construct novel operators, and these operators have given rise to intriguing subclasses of functions that have yielded practical and motivating results (see, [27][28][29][30][31][32][33]). Using Ruscheweyh and Salagean differential operators, several studies (see, for example, [34]) have generated fuzzy differential subordination.…”

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.…”

On Certain Analogues of Noor Integral Operators Associated with Fractional Integrals

“…Many other useful studies are introduced in the field of analytic functions including the fractional integral operator and its applications (see [29][30][31]).…”