Abstract
(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference26 articles.
1. Subclasses of Univalent Functions, Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1, Lecture Notes in Mathematics, Volume 1013;Salagean,1983
2. On univalent functions defined by a generalized Sălăgean operator
3. Univalent functions formulated by the Salagean-difference operator;Ibrahim;Int. J. Anal. Appl.,2019
4. Conformable differential operator generalizes the Briot-Bouquet differential equation in a complex domain
5. New Symmetric Differential and Integral Operators Defined in the Complex Domain