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Some properties for integro-differential operator defined by a fractional formal.
Zainab E Abdulnaby1, Rabha W Ibrahim2, Adem Kılıçman3
1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor Malaysia.
Springerplus
|July 8, 2016
Summary
Researchers explored a new fractional differential operator to analyze geometric properties of analytic univalent functions. This study advances understanding in fractional calculus and geometric function theory.
Area of Science:
- Mathematics
- Fractional Calculus
- Geometric Function Theory
Background:
- Growing interest in fractional calculus, including operators, polynomials, and special functions.
- Applications of fractional calculus extend beyond pure mathematics to various scientific fields.
Purpose of the Study:
- To investigate a generalized integro-differential operator.
- To define this operator using a fractional differential operator.
- To study the geometric properties of new subclasses of analytic univalent functions using this operator.
Main Methods:
- Definition of a generalized integro-differential operator.
- Application of the operator to analytic univalent functions.
- Analysis of geometric properties derived from the operator's action.
Main Results:
- Introduction of a novel generalized integro-differential operator.
- Demonstration of the operator's utility in defining new subclasses of analytic univalent functions.
- Characterization of specific geometric properties associated with these function subclasses.
Conclusions:
- The study successfully defines and applies a new fractional integro-differential operator.
- New subclasses of analytic univalent functions with distinct geometric properties have been identified.
- The findings contribute to the ongoing research in fractional calculus and its geometric applications.
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