Advances in Discrete-Fractional Mathematics and Its Application

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

Deadline for manuscript submissions: 31 March 2027 | Viewed by 739

Editors


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Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, Mexico
Interests: discrete mathematics; graph theory; differential equations; fractional differential equations; mathematical modelling in biology processes; ecoepidemiology
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, México
Interests: geometry; discrete mathematics

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Guest Editor
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, México
Interests: offensive alliances; zero-divisor graph; commutative rings; automorphism; transitivity

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Guest Editor
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, México
Interests: complex and hypercomplex analysis; boundary value problems and singular integral equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Discrete mathematics has seen newfound advancements in recent years, with the advent of increasingly powerful computers and the development of more efficient algorithm applications in different areas of knowledge making an increasingly growing cohort of researchers turn to this broad field, which includes graph theory, combinatorics, discrete modeling, cellular automata, etc., since it has contributed to the understanding and solution of real problems.

I am pleased to invite you to publish research papers in this Special Issue of Axioms, entitled “Advances in Discrete-Fractional Mathematics and Its Application”. This Special Issue aims to provide a space for the publication of high-quality papers in the area of discrete mathematics, including those that emphasize its applications in different areas of human knowledge (chemistry, biology, economics, engineering, etc.), provided that the advances discussed contribute to the expansion of theoretical knowledge or applications in this area of mathematics.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Graph theory (studies of indices, domination, alliances, hyperbolicity, convexity, spectral theory, chemistry graphs), and its applications;
  • Discrete geometry and its applications;
  • Discrete dynamic systems and their application;
  • Fractional and Fractal differential equations and their applications.

Dr. Juan Carlos Hernández Gómez
Dr. José Luis Sánchez Santiesteban
Dr. Omar Rosario−Cayetano
Dr. Ricardo Abreu-Blaya
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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.

Keywords

  • graph theory
  • domination theory
  • spectral graph theory
  • discrete dynamical systems
  • fractional differential equations
  • fractal differential equations

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Published Papers (1 paper)

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Research

21 pages, 926 KB  
Article
Admissible Convexity for Time-Varying Fractional Lyapunov Inequalities
by Jiale Chen, Osama F. Abdel Aal, Jairo Viola and Weigang Sun
Axioms 2026, 15(8), 581; https://doi.org/10.3390/axioms15080581 - 3 Aug 2026
Viewed by 226
Abstract
Fractional Lyapunov inequalities provide an effective tool for stability analysis of fractional-order systems, since classical chain and product rules are not directly applicable to fractional operators. This paper investigates admissible convexity conditions for time-varying Lyapunov functions in continuous Caputo and discrete nabla fractional [...] Read more.
Fractional Lyapunov inequalities provide an effective tool for stability analysis of fractional-order systems, since classical chain and product rules are not directly applicable to fractional operators. This paper investigates admissible convexity conditions for time-varying Lyapunov functions in continuous Caputo and discrete nabla fractional settings. It is shown that state convexity alone is insufficient: a historical ordering condition is needed to ensure the proper sign of the memory terms. The continuous inequality is characterized by a weighted integral of historical residuals, whereas the discrete nabla counterpart is characterized by a weighted sum over historical grid points. Reverse inequalities for concave functions are also derived under reversed ordering conditions. Product-form inequalities with nonnegative convex state factors and nonnegative nonincreasing time factors are recovered as natural admissible cases. Numerical examples and Lyapunov applications are presented to verify the results. Full article
(This article belongs to the Special Issue Advances in Discrete-Fractional Mathematics and Its Application)
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