Dear Colleagues,

This Special Issue is a follow-up to the first volume, entitled "Fractional Calculus and Hypergeometric Functions in Complex Analysis", which was well received. This new initiative, which builds upon the initial idea of the previous Special Issue by enlarging the focus of the targeted research, attempts to collect the most recent advancements in research regarding fractional calculus or/and quantum calculus combined with special functions in studies related to complex analysis.

Fractional calculus is a known and prolific tool in various scientific and engineering domains, as well as in theoretical studies regarding different branches of mathematics. In particular, comprehensive research has developed within the domain of geometric function theory, with the inclusion of fractional calculus. Furthermore, notable results have been obtained through enhancing investigative tools with quantum calculus aspects and through the impressive characteristics of special functions, among which hypergeometric functions are the most notable type. 

Scholars with an interest in any of these topics or in combining them with applications in other domains related to complex analysis are encouraged to submit their research in order to further the success of this Special Issue.

The topics to be covered include, but are not restricted to, the following:

• New definitions and applications in fractional calculus and quantum calculus operators;
• Applications of fractional calculus involving various special functions in complex analysis topics;
• Applications of quantum calculus involving various special functions in complex analysis topics;
• Orthogonal polynomials, including Jacobi polynomials and their special cases, 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 special functions in differential subordinations and superordiantions and their special forms of strong differential subordination and superordination and fuzzy differential subordiantion and superordination;
• Different applications of quantum calculus combined with fractional calculus and/or special functions in geometric function theory.

Prof. Dr. Gheorghe Oros
Dr. Georgia Irina Oros
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

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.

• univalent functions
• special functions
• fractional operator
• q–operator
• differential subordination
• differential superordination
• quantum calculus