Third-order differential subordination and superordination involving a fractional operator

Abstract

Abstract:The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

“…Motivated by the numerous allowances of the fractional derivative operators which have newly been reflected by many authors, here, we purposed two operators involving the generalized hypergeometric-type function and the generalized Beta function. Various studies can be found in [12,13,14].…”

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

“…This class implied several well known classes such as the starlike type. Recently, the authors have defined a new fractional integral operator based on the fractional hypergeometric function [37]. Other applications can be located in [38][39][40][41].…”

Third-Order Differential Subordination and Differential Superordination Results for Analytic Functions Involving the Srivastava-Attiya Operator

“…The recent work due to Tang et al [18,20] on third order differential subordination attracted to many researchers in this field. For example see [4,8,9,14,18,19,20,13,11]. In the present paper we considered suitable classes of admissible functions associated with Srivastava-Attiya operator and obtained sufficient conditions on the normalized analytic function f such that Sandwich-type subordination of the following form holds:…”