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Symmetry
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Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities
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Symmetry Applied in Fractional Dynamics, 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 March 2024) | Viewed by 4738

Special Issue Editors

Dr. Pshtiwan Othman Mohammed

E-Mail Website
Guest Editor
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Kurdistan Region, Iraq
Interests: fractional calculus; discrete fractional calculus; integral inequalities; special functions; numerical analysis
Dr. Soubhagya Kumar Sahoo

E-Mail Website
Co-Guest Editor
Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University, Bhubaneswar 751030, Odisha, India
Interests: fractional calculus; discrete fractional calculus; integral inequalities; special functions
Dr. Artion Kashuri

E-Mail Website
Co-Guest Editor
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
Interests: fractional calculus; quantum calculus; integral inequalities; special functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

During the last three decades, symmetry in fractional calculus/discrete fractional calculus, dynamics and inequalities has been studied extensively. As a matter of fact, fractional derivatives and integrals provide a much better tool for the description of the memory and hereditary properties of various materials and processes than integer derivatives. Engineers and scientists have developed new precise models that involve fractional differential equations and inequalities. These models have been applied successfully, e.g., in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex media, electrical circuits, electroanalytical chemistry and control theory. The main purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical developments in the field of symmetry applied in fractional calculus–dynamics and inequalities with their applications.

Dr. Pshtiwan Othman Mohammed
Dr. Soubhagya Kumar Sahoo
Dr. Artion Kashuri
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. 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 calculus
  • integral inequalities (ordinary and fractional)
  • discrete fractional calculus
  • monotonicity, positivity and convexity analysis
  • symmetry and dynamical systems
  • existence and uniqueness of solutions

Published Papers (5 papers)

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Research

12 pages, 413 KiB  
Article
The Generalized Fractional-Order Fisher Equation: Stability and Numerical Simulation
by Bilge İnan
Symmetry 2024, 16(4), 393; https://doi.org/10.3390/sym16040393 - 27 Mar 2024
Viewed by 494
Abstract
This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method [...] Read more.
This study examines the stability and numerical simulation of the generalized fractional-order Fisher equation. The equation serves as a mathematical model describing population dynamics under the influence of factors such as natural selection and migration. We propose an implicit exponential finite difference method to solve this equation, considering the conformable fractional derivative. Furthermore, we analyze the stability of the method through theoretical considerations. The method involves transforming the problem into systems of nonlinear equations at each time since our method is an implicit method, which is then solved by converting them into linear equations systems using the Newton method. To test the accuracy of the method, we compare the results obtained with exact solutions and with those available in the literature. Additionally, we examine the symmetry of the graphs obtained from the solution to examine the results. The findings of our numerical simulations demonstrate the effectiveness and reliability of the proposed approach in solving the generalized fractional-order Fisher equation. Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
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15 pages, 969 KiB  
Article
On Conformable Fractional Milne-Type Inequalities
by Rui Ying, Abdelghani Lakhdari, Hongyan Xu, Wedad Saleh and Badreddine Meftah
Symmetry 2024, 16(2), 196; https://doi.org/10.3390/sym16020196 - 07 Feb 2024
Viewed by 568
Abstract
Building upon previous research in conformable fractional calculus, this study introduces a novel identity. Using this identity as a foundation, we derive a set of conformable fractional Milne-type inequalities specifically designed for differentiable convex functions. The obtained results recover some existing inequalities in [...] Read more.
Building upon previous research in conformable fractional calculus, this study introduces a novel identity. Using this identity as a foundation, we derive a set of conformable fractional Milne-type inequalities specifically designed for differentiable convex functions. The obtained results recover some existing inequalities in the literature by fixing some parameters. These novel contributions aim to enrich the analytical tools available for studying convex functions within the realm of conformable fractional calculus. The derived inequalities reflect an inherent symmetry characteristic of the Milne formula, further illustrating the balanced and harmonious mathematical structure within these frameworks. We provide a thorough example with graphical representations to support our findings, offering both numerical insights and visual confirmation of the established inequalities. Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
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13 pages, 297 KiB  
Article
Some Fractional Integral Inequalities by Way of Raina Fractional Integrals
by Miguel Vivas-Cortez, Asia Latif and Rashida Hussain
Symmetry 2023, 15(10), 1935; https://doi.org/10.3390/sym15101935 - 19 Oct 2023
Viewed by 616
Abstract
In this research, some novel Hermite–Hadamard–Fejér-type inequalities using Raina fractional integrals for the class of ϑ-convex functions are obtained. These inequalities are more comprehensive and inclusive than the corresponding ones present in the literature. Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
23 pages, 709 KiB  
Article
Symmetry Analyses of Epidemiological Model for Monkeypox Virus with Atangana–Baleanu Fractional Derivative
by Tharmalingam Gunasekar, Shanmugam Manikandan, Vediyappan Govindan, Piriadarshani D, Junaid Ahmad, Walid Emam and Isra Al-Shbeil
Symmetry 2023, 15(8), 1605; https://doi.org/10.3390/sym15081605 - 19 Aug 2023
Cited by 2 | Viewed by 1104
Abstract
The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study [...] Read more.
The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and rodent populations. An iterative method and the fixed-point theorem are used to prove the existence and uniqueness of the symmetry model’s system of solutions. It shows that the symmetry model has equilibrium points when there are epidemics and no diseases. As well as the local asymptotic stability of the disease-free equilibrium point, conditions for the endemic equilibrium point’s existence have also been demonstrated. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimal conditions are acquired Pontryagin’s maximum principle is used. Then, the stability of the symmetry model is discussed at monkeypox-free and endemic equilibrium points with treatment strategies to control the spread of the disease. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic. Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
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15 pages, 490 KiB  
Article
Some New Hermite-Hadamard Type Inequalities Pertaining to Fractional Integrals with an Exponential Kernel for Subadditive Functions
by Artion Kashuri, Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Eman Al-Sarairah and Y. S. Hamed
Symmetry 2023, 15(3), 748; https://doi.org/10.3390/sym15030748 - 18 Mar 2023
Cited by 2 | Viewed by 847
Abstract
The class of symmetric function interacts extensively with other types of functions. One of these is the class of convex functions, which is closely related to the theory of symmetry. In this paper, we obtain some new fractional Hermite–Hadamard inequalities with an exponential [...] Read more.
The class of symmetric function interacts extensively with other types of functions. One of these is the class of convex functions, which is closely related to the theory of symmetry. In this paper, we obtain some new fractional Hermite–Hadamard inequalities with an exponential kernel for subadditive functions and for their product, and some known results are recaptured. Moreover, using a new identity as an auxiliary result, we deduce several inequalities for subadditive functions pertaining to the new fractional integrals involving an exponential kernel. To validate the accuracy of our results, we offer some examples for suitable choices of subadditive functions and their graphical representations. Full article
(This article belongs to the Special Issue Symmetry Applied in Fractional Dynamics, Fractional Calculus and Inequalities)
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