Recent Advances in General Integral Operators

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 2800

Special Issue Editors


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Guest Editor
Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
Interests: univalent functions; convex functions; analytic functions; starlike functions; integral operators
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. Department of Informatics, Mathematicsand Electronics, Faculty of Science and Engineering, "1 Decembrie 1918" University of Alba Iulia, 510009 Alba Iulia, Romania
2. Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Interests: systems and control; time-varying systems; dynamical systems; difference equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue focuses on integral operators in a general framework.

It is well known that integral operators are indispensable tools in various scientific fields, such as real analysis, functional analysis, complex analysis, theory of dynamic systems, and other subjects of mathematical approaches.

We invite scientists and engineers from academia to contribute with original results related to integral operators.

The topics of interest in this Special Issue include but are not limited to:

  • Univalence conditions for integral operators
  • Fractional integral operators
  • conformable integral operators
  • Differential operators
  • Singular integral operators
  • Fourier integral operators
  • Hilbert–Schmidt integral operator
  • Numerical methods to approximate integral operators
  • Learning integral operators
  • Integral operators in inequalities
  • Integral operators via convexity
  • Integral operators and its applications

Prof. Dr. Daniel Valer Breaz
Dr. Ioan-Lucian Popa
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.

Published Papers (3 papers)

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Research

11 pages, 310 KiB  
Article
Further Generalizations of Some Fractional Integral Inequalities
by Dong Chen, Matloob Anwar, Ghulam Farid and Hafsa Yasmeen
Fractal Fract. 2023, 7(6), 489; https://doi.org/10.3390/fractalfract7060489 - 20 Jun 2023
Viewed by 681
Abstract
This paper aims to establish generalized fractional integral inequalities for operators containing Mittag–Leffler functions. By applying (α,hm)p-convexity of real valued functions, generalizations of many well-known inequalities are obtained. Hadamard-type inequalities for various classes of functions are given in particular cases. Full article
(This article belongs to the Special Issue Recent Advances in General Integral Operators)
12 pages, 326 KiB  
Article
Some Estimates of k-Fractional Integrals for Various Kinds of Exponentially Convex Functions
by Yonghong Liu, Matloob Anwar, Ghulam Farid and Hala Safdar Khan
Fractal Fract. 2023, 7(4), 297; https://doi.org/10.3390/fractalfract7040297 - 29 Mar 2023
Viewed by 827
Abstract
In this paper, we aim to find unified estimates of fractional integrals involving Mittag–Leffler functions in kernels. The results obtained in terms of fractional integral inequalities are provided for various kinds of convex and related functions. A variant of Hadamard-type inequality is also [...] Read more.
In this paper, we aim to find unified estimates of fractional integrals involving Mittag–Leffler functions in kernels. The results obtained in terms of fractional integral inequalities are provided for various kinds of convex and related functions. A variant of Hadamard-type inequality is also presented, which shows the upper and lower bounds of fractional integral operators of many kinds. The results of this paper are directly linked with many recently published inequalities. Full article
(This article belongs to the Special Issue Recent Advances in General Integral Operators)
20 pages, 351 KiB  
Article
Examining the Hermite–Hadamard Inequalities for k-Fractional Operators Using the Green Function
by Çetin Yildiz and Luminiţa-Ioana Cotîrlă
Fractal Fract. 2023, 7(2), 161; https://doi.org/10.3390/fractalfract7020161 - 6 Feb 2023
Cited by 6 | Viewed by 812
Abstract
For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities [...] Read more.
For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities to the convex and monotone functions, new Hermite–Hadamard type inequalities are established. Furthermore, a different form of the Hermite–Hadamard inequality is also obtained by using this novel approach. In conclusion, we believe that the approach presented in this paper will inspire more research in this area. Full article
(This article belongs to the Special Issue Recent Advances in General Integral Operators)
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