Fractional Calculus and Hypergeometric Functions in Complex Analysis
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: closed (15 March 2023) | Viewed by 19813
Special Issue Editors
Interests: special classes of univalent functions; differential subordinations and superordinations; differential operators; integral operators; differential-integral operators
Special Issues, Collections and Topics in MDPI journals
Interests: special classes of univalent functions; differential subordinations and superordinations; differential operators; integral operators; differential–integral operators
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Fractional calculus has had a powerful impact on recent research, having many applications in different branches of science and engineering. Various branches of mathematics are also influenced by fractional calculus. Applications in complex analysis research are comprehensive, and interesting new results have been obtained in studies involving univalent functions theory.
This Special Issue aims to gather new research outcomes combining this prolific tool with another that generates exciting results when integrated into studies: hypergeometric functions.
The study of hypergeometric functions dates back 200 years. They appear in the work of Euler, Gauss, Riemann, and Kummer. Interest in hypergeometric functions has grown in the last few decades due to hypergeometric functions’ applications in a large variety of scientific domains and many areas of mathematics. Hypergeometric functions were linked to the theory of univalent functions by L. de Branges’ proof of Bieberbach’s conjecture, published in 1985, which uses the generalized hypergeometric function. After this connection was established, hypergeometric functions was studied intensely using geometric function theory.
Quantum calculus is also involved in studies alongside fractional calculus tools and different hypergeometric functions.
Researchers interested in any of these topics or a combination of them and their applications in different areas concerning complex analysis are welcome to submit their findings and contribute to the success of this Special Issue.
Topics include but are not limited to:
- New definitions and applications in fractional calculus operators;
- Applications of fractional calculus involving hypergeometric functions in geometric function theory;
- Orthogonal polynomials, including Jacobi and their special functions, including Legendre polynomials, Chebyshev polynomials, and Gegenbauer polynomials;
- Applications of logarithmic, exponential, and trigonometric functions regarding univalent functions theory;
- Applications of gamma, beta, and digamma functions;
- Applications of fractional calculus and hypergeometric functions in differential subordinations and superordinations and their special forms of strong differential subordination and superordination and fuzzy differential subordination and superordination;
- Applications of quantum calculus involving fractional calculus in geometric function theory;
- Applications of quantum calculus involving hypergeometric functions in complex analysis.
Prof. Dr. Gheorghe Oros
Dr. Georgia Irina Oros
Guest Editors
Manuscript Submission Information
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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- univalent functions
- special functions
- fractional operators
- differential subordination
- differential superordination
- quantum calculus
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