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Fractal Fract
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Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition
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Mathematical Inequalities in Fractional Calculus and Applications, 2nd 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 May 2025 | Viewed by 1099

Special Issue Editors

Dr. Seth Kermausuor

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL, 36101, USA
Interests: mathematical inequalities; fractional calculus; time scales; modeling; analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Eze Nwaeze

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA
Interests: mathematical inequalities; fractional calculus; time scale theory; growth properties of complex polynomials
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Inequalities of any type play a very important role in various aspects of mathematical analysis, such as approximation theory and the theory of differential equations. The theory of fractional calculus, which deals with the study and applications of the derivatives and integrals of arbitrary orders, has gained considerable attention due to its numerous applications in the applied sciences.

In recent years, fractional differential equations have been used frequently in the modelling of real systems in numerous fields of applied sciences. To study the existence, uniqueness, and stability of solutions to a system of fractional differential equation inequalities involving derivatives and integrals of arbitrary powers, also known as fractional inequalities, have been used. Additionally, fractional inequalities have been used to find the upper and lower bounds of solutions to a system of fractional differential equations. In addition, fractional inequalities are also used in the fields of probability, numerical quadrature, and many more. Over the years, many authors have established several generalizations of the various classical inequalities to fractional calculus in the literature.

The goal of this Special Issue is to continue to the advancing of the research on mathematical inequalities in fractional calculus by assembling both original research and review articles on the subject and its related topics. Topics that are invited for submission include (but are not limited to) the following:

  • Fractional integral inequalities;
  • Inequalities of generalized functions in fractional calculus;
  • Q-calculus;
  • Inequalities in fractional calculus on time scales;
  • Fractional order derivatives;
  • Applications of fractional inequalities;
  • Fractals;
  • Non-local mathematical models;
  • Fractional complicated systems.

Dr. Seth Kermausuor
Dr. Eze Nwaeze
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 calculus
  • caputo derivative
  • riemann-liouville derivative
  • discrete fractional calculus
  • fractals
  • fractional differential equations
  • mathematical inequalities
  • time scales

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Related Special Issue

Published Papers (2 papers)

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Research

32 pages, 510 KiB  
Article
Fractional Hermite–Hadamard, Newton–Milne, and Convexity Involving Arithmetic–Geometric Mean-Type Inequalities in Hilbert and Mixed-Norm Morrey Spaces ℓq(·)(Mp(·),v(·)) with Variable Exponents
by Waqar Afzal, Mujahid Abbas, Daniel Breaz and Luminiţa-Ioana Cotîrlă
Fractal Fract. 2024, 8(9), 518; https://doi.org/10.3390/fractalfract8090518 - 30 Aug 2024
Viewed by 373
Abstract
Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is [...] Read more.
Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is crucial in mathematical analysis. In this note, we develop various new bounds and refinements of different well-known inequalities involving Hilbert spaces in a tensor framework as well as mixed Moore norm spaces with variable exponents. The article begins with Newton–Milne-type inequalities for differentiable convex mappings. Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. To obtain all these results, we use Riemann–Liouville fractional integrals and develop several new identities for these operator inequalities. Furthermore, we present some examples and consequences for transcendental functions. Moreover, we developed the Hermite–Hadamard inequality in a new and significant way by using mixed-norm Moore spaces with variable exponent functions that have not been developed previously with any other type of function space apart from classical Lebesgue space. Mathematical inequalities supporting tensor Hilbert spaces are rarely examined in the literature, so we believe that this work opens up a whole new avenue in mathematical inequality theory. Full article
(This article belongs to the Special Issue Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition)
16 pages, 299 KiB  
Article
On New Generalized Hermite–Hadamard–Mercer-Type Inequalities for Raina Functions
by Zeynep Çiftci, Merve Coşkun, Çetin Yildiz, Luminiţa-Ioana Cotîrlă and Daniel Breaz
Fractal Fract. 2024, 8(8), 472; https://doi.org/10.3390/fractalfract8080472 - 13 Aug 2024
Viewed by 507
Abstract
In this research, we demonstrate novel Hermite–Hadamard–Mercer fractional integral inequalities using a wide class of fractional integral operators (the Raina fractional operator). Moreover, a new lemma of this type is proved, and new identities are obtained using the definition of convex function. In [...] Read more.
In this research, we demonstrate novel Hermite–Hadamard–Mercer fractional integral inequalities using a wide class of fractional integral operators (the Raina fractional operator). Moreover, a new lemma of this type is proved, and new identities are obtained using the definition of convex function. In addition to a detailed derivation of a few special situations, certain known findings are summarized. We also point out that some results in this study, in some special cases, such as setting α=0=φ,γ=1, and w=0,σ(0)=1,λ=1, are more reasonable than those obtained. Finally, it is believed that the technique presented in this paper will encourage additional study in this field. Full article
(This article belongs to the Special Issue Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition)
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