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Volume 10
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Article

Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions

by
Alina Alb Lupaş
*,† and
Georgia Irina Oros
†
Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2022, 10(5), 705; https://doi.org/10.3390/math10050705
Submission received: 1 February 2022 / Revised: 22 February 2022 / Accepted: 23 February 2022 / Published: 23 February 2022
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
Versions Notes

Abstract

The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions to belong to this class are determined and the class is investigated considering aspects regarding coefficient bounds as well as partial sums of these functions. Distortion properties of the functions belonging to the class are proved and radii estimates are established for starlikeness and convexity properties of the class.
Keywords: analytic function; fractional integral; confluent hypergeometric function; coefficient bounds; partial sum; radii of starlikeness and convexity analytic function; fractional integral; confluent hypergeometric function; coefficient bounds; partial sum; radii of starlikeness and convexity

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MDPI and ACS Style

Lupaş, A.A.; Oros, G.I. Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions. Mathematics 2022, 10, 705. https://doi.org/10.3390/math10050705

AMA Style

Lupaş AA, Oros GI. Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions. Mathematics. 2022; 10(5):705. https://doi.org/10.3390/math10050705

Chicago/Turabian Style

Lupaş, Alina Alb, and Georgia Irina Oros. 2022. "Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions" Mathematics 10, no. 5: 705. https://doi.org/10.3390/math10050705

APA Style

Lupaş, A. A., & Oros, G. I. (2022). Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions. Mathematics, 10(5), 705. https://doi.org/10.3390/math10050705

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