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Symmetry
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Symmetry in Fractional Calculus and Inequalities
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Symmetry in Fractional Calculus and Inequalities

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (15 July 2022) | Viewed by 7848

Special Issue Editor

Prof. Dr. Hüseyin Budak

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Interests: fractional calculus; quantum calculus; integral inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, the investigation with fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. Fractional calculus has become an important tool for modeling analysis and has played a very important role in various fields, such as fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. There are many definitions of fractional integrals and derivatives in the literature, and many important inequalities have been obtained for these definitions. On the other hand, the concept of symmetry is a beauty structure used to describe the environment and problems of the real world, as well as to strengthen the relationship between mathematical science and applied science such as physics and engineering. Therefore, the concept of symmetry exists in fractional calculus as in many other fields. In this special issue, the concept of Symmetry will be in the foreground.

The purpose of this Special Issue is to publish original and high-quality papers covering the latest advances in the theory of Fractional calculus with symmetry as well as generalizations of fractional important inequalities.

The issue of the subject will be focused but not limited to:

  • Fractional integral inequalities;
  • Symmetry in fractional operators and models;
  • q-inequalities via fractional calculus;
  • Fractional differential equations and inclusions;
  • Symmetry on fractal and fractional differential operators;
  • Discrete fractional equations;
  • Fractional Calculus- new fractional definitions, their properties and applications;
  • Fractional (p, q)-calculus

Dr. Hüseyin Budak
Guest Editor

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. Symmetry 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

  • Fractional integral inequalities
  • Symmetry in fractional operators and models
  • q-inequalities via fractional calculus
  • Fractional differential equations and inclusions
  • Symmetry on fractal and fractional differential operators
  • Discrete fractional equations
  • Fractional Calculus- new fractional definitions, their properties and applications
  • Fractional (p, q)-calculus

Published Papers (5 papers)

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Research

9 pages, 266 KiB  
Article
Stability of Nonlinear Fractional Delay Differential Equations
by D. A. Refaai, M. M. A. El-Sheikh, Gamal A. F. Ismail, Mohammed Zakarya, Ghada AlNemer and Haytham M. Rezk
Symmetry 2022, 14(8), 1606; https://doi.org/10.3390/sym14081606 - 04 Aug 2022
Cited by 2 | Viewed by 1242
Abstract
This article discusses several forms of Ulam stability of nonlinear fractional delay differential equations. Our investigation is based on a generalised Gronwall’s inequality and Picard operator theory. Implementations are provided to demonstrate the stability results obtained for finite intervals. Full article
(This article belongs to the Special Issue Symmetry in Fractional Calculus and Inequalities)
27 pages, 485 KiB  
Article
On Fractional Newton Inequalities via Coordinated Convex Functions
by Pınar Kösem, Hasan Kara, Hüseyin Budak, Muhammad Aamir Ali and Kamsing Nonlaopon
Symmetry 2022, 14(8), 1526; https://doi.org/10.3390/sym14081526 - 26 Jul 2022
Cited by 1 | Viewed by 817
Abstract
In this paper, firstly, we present an integral identity for functions of two variables via Riemann–Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are [...] Read more.
In this paper, firstly, we present an integral identity for functions of two variables via Riemann–Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the Hölder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained inequalities. Full article
(This article belongs to the Special Issue Symmetry in Fractional Calculus and Inequalities)
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13 pages, 927 KiB  
Article
A Semi-Analytical Method to Investigate Fractional-Order Gas Dynamics Equations by Shehu Transform
by Rasool Shah, Azzh Saad Alshehry and Wajaree Weera
Symmetry 2022, 14(7), 1458; https://doi.org/10.3390/sym14071458 - 16 Jul 2022
Cited by 11 | Viewed by 1509
Abstract
This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an [...] Read more.
This work aims at a new semi-analytical method called the variational iteration transformation method for solving nonlinear homogeneous and nonhomogeneous fractional-order gas dynamics equations. The Shehu transformation and the iterative technique are applied to solve the suggested problems. The proposed method has an advantage over existing approaches because it does not require additional materials or computations. Four problems are used to test the authenticity of the proposed method. Using the suggested method, the solution proves to be more accurate. The proposed method can be implemented to solve many nonlinear fractional order problems because it has a straightforward implementation. Full article
(This article belongs to the Special Issue Symmetry in Fractional Calculus and Inequalities)
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14 pages, 294 KiB  
Article
Some New Quantum Hermite-Hadamard Type Inequalities for s-Convex Functions
by Ghazala Gulshan, Hüseyin Budak, Rashida Hussain and Kamsing Nonlaopon
Symmetry 2022, 14(5), 870; https://doi.org/10.3390/sym14050870 - 24 Apr 2022
Cited by 4 | Viewed by 1421
Abstract
In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities for s-convex functions by utilizing newly defined Tq-integrals. Then, by using obtained inequality, we establish a new Hermite–Hadamard inequality for coordinated s1,s2-convex functions. [...] Read more.
In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities for s-convex functions by utilizing newly defined Tq-integrals. Then, by using obtained inequality, we establish a new Hermite–Hadamard inequality for coordinated s1,s2-convex functions. The results obtained in this paper provide significant extensions of other related results given in the literature. Finally, some examples are given to illustrate the result obtained in this paper. These types of analytical inequalities, as well as solutions, apply to different areas where the concept of symmetry is important. Full article
(This article belongs to the Special Issue Symmetry in Fractional Calculus and Inequalities)
16 pages, 835 KiB  
Article
Hadamard–Mercer, Dragomir–Agarwal–Mercer, and Pachpatte–Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications
by Soubhagya Kumar Sahoo, Ravi P. Agarwal, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Kamsing Nonlaopon and Khadijah M. Abualnaja
Symmetry 2022, 14(4), 836; https://doi.org/10.3390/sym14040836 - 18 Apr 2022
Cited by 11 | Viewed by 1543
Abstract
Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard–Mercer, Pachpatte–Mercer, and [...] Read more.
Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard–Mercer, Pachpatte–Mercer, and Dragomir–Agarwal–Mercer types containing an exponential kernel. In this regard, the inequality proved by Jensen and Mercer plays a major role in our main results. Integral inequalities involving convexity have a wide range of applications in several domains of mathematics where symmetry is important. Both convexity and symmetry are closely linked with each other; when working on one of the topics, you can apply what you have learned to the other. We consider a new identity for differentiable mappings and present its companion bound for the Dragomir–Agarwal–Mercer type inequality employing a convex function. Applications involving matrices are presented. Finally, we conclude our article and discuss its future scope. Full article
(This article belongs to the Special Issue Symmetry in Fractional Calculus and Inequalities)
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