Fractional Integral Inequalities and Applications, 3rd Edition

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 1069

Special Issue Editors


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Department of Mathematical Engineering, Polytechnic University of Tirana, 1001 Tirana, Albania
Interests: mathematical inequalities; special functions; approximation theory; fractional calculus; applied mathematics
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Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modelling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The theory of inequalities represents a long-standing topic in many areas of mathematics and remains an attractive research area, with applications spanning fractional calculus, quantum calculus, operator theory, numerical analysis, operator equations, network theory and quantum information theory. In recent years, this area of research has garnered significant attention, and the interplay between individual aspects of this theory has enriched all of these domains.

The numerical integration and estimation of definite integrals is vital in applied sciences. Among the numerical techniques, Simpson's rules are particularly notable.

This Special Issue aims to collect original research papers that address all areas of mathematics and the numerous applications concerned with inequalities or their basic role. The research results presented should be related to the improvement, extension and generalization of classical and recent inequalities, and highlight their application in functional analysis, nonlinear functional analysis, multivariate analysis, quantum calculus, statistics, probability and other fields.

Please note that all submitted papers should be within the scope of the journal.

Dr. Artion Kashuri
Prof. Dr. Hari Mohan Srivastava
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.

Keywords

  • fractional integral inequalities
  • generalized convexity
  • numerical estimations
  • quantum calculus
  • multivariate analysis
  • means
  • operator theory
  • approximation theory

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Published Papers (1 paper)

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Research

23 pages, 504 KiB  
Article
Fractional Reverse Inequalities Involving Generic Interval-Valued Convex Functions and Applications
by Bandar Bin-Mohsin, Muhammad Zakria Javed, Muhammad Uzair Awan, Badreddine Meftah and Artion Kashuri
Fractal Fract. 2024, 8(10), 587; https://doi.org/10.3390/fractalfract8100587 - 3 Oct 2024
Viewed by 627
Abstract
The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus [...] Read more.
The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus and a generic class of interval-valued convexity. We introduce the concept of I.V-(,) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(,) convexity to derive new improvements of the H-H- and Fejer and Pachpatte-like inequalities. Our results are quite unified; by substituting the different values of parameters, we obtain a blend of new and existing inequalities. These results are fruitful for establishing bounds for I.V R-L integral operators. Furthermore, we discuss various implications of our findings, along with numerical examples and simulations to enhance the reliability of our results. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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