Theoretical Advances in Fractional Calculus

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 25 October 2024 | Viewed by 141

Special Issue Editors

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Guest Editor
Department of Mathematics, Donghua University, Shanghai, China
Interests: special functions; fractional calculus; functional differential equations

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Guest Editor
Department of Mathematical and Functional Analysis, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
Interests: approximation theory; continued fractions and their generalizations; special functions; numerical analysis
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Special Issue Information

Dear Colleagues,

Fractional calculus is an important branch of modern mathematics. Through centuries of development, a rich theory has been developed, providing  powerful tools not only for mathematicians from different fields, but also for physicists and engineers. In this Special Issue of Axioms, we wish to further explore the theory of fractional calculus along the following three directions:

(1) To further study the mathematical properties of the known fractional operators and their q-analogues or discrete analogues.

(2) To discover specific applications of the ideas, methods, and results of fractional calculus to such areas of pure mathematics as special functions, differential equations, harmonic analysis, functional analysis, number theory, combinatorics, etc.

(3) To find solutions regarding the open problems in fractional calculus.

Our goal is to expand the theoretical foundations of fractional calculus, to strengthen its connections with other branches of modern mathematics, and to find some surprisingly exciting examples. We hope to gather experts in various fields, especially young researchers, focusing on the above issues and to promote the development of fractional calculus.  We invite high-quality original research papers, as well as survey papers relating to the topic of this issue.

Dr. Min-Jie Luo
Prof. Dr. Roman Dmytryshyn
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at 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. Axioms 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 2400 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.


  • fractional calculus
  • generalized fractional calculus
  • fractional differential equations
  • fractional integral equations
  • special functions in one or several variables
  • special functions in matrix arguments
  • asymptotic expansions
  • orthogonal expansions
  • q-series 
  • open problems

Published Papers

This special issue is now open for submission.
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