MODELLING AND APPLICATIONS INVOLVING FRACTIONAL
DERIVATIVES AND MITTAG-LEFFLER FUNCTIONS

Dr. Bonala Madhavi1, Dr. D. Pushpa2
1Assistant Professor of Mathematics,
Pingle Government College for Women (Autonomous),
Hanamkonda, Telangana, India
2Assistant Professor of Mathematics,
Government Degree College for Women (Autonomous),
Begumpet, Hyderabad, Telangana, India

Abstract


Abstract. The aim of this paper is to introduce and systematically investigate a new subclass TS(χ,σ,ς) of analytic and univalent functions with negative coefficients defined in the open unit disk U={z∈C:|z|<1}. This newly established class is formulated by leveraging the specialized properties of fractional derivative operators integrated with the versatile Mittag-Leffler function. For functions belonging to this subclass, we derive fundamental geometric and analytic properties. Specifically, we establish sharp coefficient inequalities and prove comprehensive distortion and covering theorems. Furthermore, we determine the precise radii of starlikeness, convexity, and close-to-convexity to characterize the geometric boundaries of the class. Finally, we determine the extreme points, analyze the behavior under the Hadamard (convolution) product, and establish closure theorems. The results obtained not only generalize several existing frameworks in geometric function theory but also highlight the powerful interplay between fractional calculus and subclasses of univalent functions.

Received: 20 Nov 2023

Key Words and Phrases: Analytic functions, univalent functions, fractional derivatives, Mittag-Leffler functions, coefficient estimates, starlikeness, convexity.

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How to cite this paper?
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2023
Volume: 36
Issue: 6
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