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Fractal Fract
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Fractional Integral Inequalities and Applications, 3rd Edition
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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 4582

Special Issue Editors

Dr. Artion Kashuri

E-Mail Website
Guest Editor
Department of Mathematical Engineering, Polytechnic University of Tirana, 1001 Tirana, Albania
Interests: mathematical inequalities; special functions; approximation theory; fractional calculus; applied mathematics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
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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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

23 pages, 358 KiB  
Article
New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity
by Wedad Saleh, Hamid Boulares, Abdelkader Moumen, Hussien Albala and Badreddine Meftah
Fractal Fract. 2025, 9(1), 25; https://doi.org/10.3390/fractalfract9010025 - 3 Jan 2025
Cited by 2 | Viewed by 1120
Abstract
This paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fractional inequalities, presenting a range of results not only for fractional integrals [...] Read more.
This paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fractional inequalities, presenting a range of results not only for fractional integrals and fractal calculus, but also offering a refinement of the well-known Bullen-type inequality. We further explore the connections between generalized convexity and fractal–fractional integrals, showing how the concept of generalized convexity enables the establishment of error bounds for fractal–fractional integrals involving lower-order derivatives, with an emphasis on their applications in various fields. The findings expand the current understanding of fractal–fractional inequalities and offer new insights into the use of local fractional derivatives for analyzing functions with fractional-order properties. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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21 pages, 483 KiB  
Article
New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities
by Asfand Fahad, Zammad Ali, Shigeru Furuichi, Saad Ihsan Butt, Ayesha and Yuanheng Wang
Fractal Fract. 2024, 8(12), 728; https://doi.org/10.3390/fractalfract8120728 - 12 Dec 2024
Viewed by 713
Abstract
We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional [...] Read more.
We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional fractional integral operators (HPFIOs) and Hadamard k-fractional integral operators (HKFIOs). Moreover, we also present the results for subclasses of GA-h-CFs and show that the inequalities proved in this paper unify the results from the recent related literature. Furthermore, we compare the two generalizations in view of the fractional operator parameters that contribute to the generalizations of the results and assess the better approximation via graphical tools. Finally, we present applications of the new inequalities via HPFIOs and HKFIOs by establishing interpolation relations between arithmetic mean and geometric mean and by proving the new upper bounds for the Tsallis relative operator entropy. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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17 pages, 335 KiB  
Article
Significant Study of Fuzzy Fractional Inequalities with Generalized Operators and Applications
by Rana Safdar Ali, Humira Sif, Gauhar Rehman, Ahmad Aloqaily and Nabil Mlaiki
Fractal Fract. 2024, 8(12), 690; https://doi.org/10.3390/fractalfract8120690 - 24 Nov 2024
Viewed by 578
Abstract
There are many techniques for the extension and generalization of fractional theories, one of which improves fractional operators by means of their kernels. This paper is devoted to the most general concept of interval-valued functions, studying fractional integral operators for interval-valued functions, along [...] Read more.
There are many techniques for the extension and generalization of fractional theories, one of which improves fractional operators by means of their kernels. This paper is devoted to the most general concept of interval-valued functions, studying fractional integral operators for interval-valued functions, along with the multi-variate extension of the Bessel–Maitland function, which acts as kernel. We discuss the behavior of Hermite–Hadamard Fejér (HHF)-type inequalities by using the convex fuzzy interval-valued function (C-FIVF) with generalized fuzzy fractional operators. Also, we obtain some refinements of Hermite–Hadamard(H-H)-type inequalities via convex fuzzy interval-valued functions (C-FIVFs). Our results extend and generalize existing findings from the literature. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 3rd Edition)
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
Cited by 1 | Viewed by 1260
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-(⋏,ℏ) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(⋏,ℏ) 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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