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Symmetry
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Symmetry in New Trends for Discrete Fractional Calculus with Applications
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Symmetry in New Trends for Discrete Fractional Calculus with Applications

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

Deadline for manuscript submissions: closed (20 September 2022) | Viewed by 5825

Special Issue Editors

Dr. Ahmet Ocak Akdemir

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science and Letters, Ağrı İbrahim Çeçen University, 04100 Ağrı, Turkey
Interests: Fractional calculus; integral inequalities; convex analysis
Dr. Zakia Hammouch

E-Mail Website
Guest Editor
Ecole Normale Supéerieure de Meknés, Université Moulay Ismail, Meknes 50000, Morocco
Interests: fractional partial differential equations; fractional calculus; modeling; simulation methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematics is a useful tool that explains physical phenomena, creates a working platform for engineering sciences, and establishes relationships between concepts whose definitions are known in fields such as statistics, economics, chemistry and biology. When mathematical concepts are evaluated together with the corresponding phenomena in applied sciences, a solution-oriented approach emerges by modeling and simulating real-world problems. The significance of a real mathematical concept or method is hidden in terms of the degree to which it serves this solution-oriented approach. The effectiveness of a differential or integral equation is measured by its contribution to the solution of the real-world problem it characterizes.

When considered in this context, mathematical concepts and methods emerge as indispensable elements of applied sciences that direct our lives and enable us to continue our existence in practice by suggesting solutions to our problems. Discrete fractional calculus, which has recently become a popular subject in many fields of mathematics, especially in the fields of mathematical analysis and applied mathematics, and therefore in many applied sciences such as physics, engineering sciences, mathematical biology, statistics, control theory, chaos theory, and modeling, has brought a new dimension to its solutions.

Discrete fractional calculus is a new field in applied mathematics that arises as a result of the open problem related to solving some differential equations containing discrete fractional sums. The answer to this problem has led mathematicians to new searches as a subject that many researchers have been interested in for years. Defining discrete fractional calculus and then suggesting related discrete fractional sums with various operator definitions have made it an indispensable part of applied sciences and other branches of mathematics. Discrete difference operators propose solutions that are quite suitable for real-world problems and strengthen the relationship of mathematics with other disciplines in terms of application areas.

With this Special Issue, a new perspective on applied sciences and natural phenomena will be provided from the perspective of discrete fractional sums. In light of the concepts introduced within the scope of discrete fractional calculus, we aim to deal with a wide spectrum of topics such as chaos theory, control theory, systems of equations that schematize disease models, approximation theory, computational sciences, fluid dynamics, majorization problems, numerical analysis, stability, simulations, and regularity problems. The functionality and effectiveness of this wide range of fractional analysis will be discussed and a contribution will be made to the literature in this sense. The concept of symmetry is an aesthetic structure used to explain nature and real-world problems, as well as strengthen the relations between mathematical sciences and applied sciences such as physics and engineering. Especially in fractional analysis, it emerges in the structure and applications of operators. For this reason, the concept of symmetry will be at the forefront of the works that will take place in this Special Issue.

We plan to focus on new research and future trends in mathematical sciences in this Special Issue. We invite investigators and our participants to contribute to this Special Issue with original papers describing advances, findings and future trends in the field of mathematical sciences. In accordance with this purpose, all manuscripts must be written so as to be widely accessible to all scientists.

Potential topics include but are not limited to:

  • Computational methods via discrete fractional sums;
  • Nonlinear discrete fractional differential equations;
  • Fractional differential equations;
  • Mathematical modeling and optimization;
  • Numerical solution methods;
  • Operations research;
  • Chaos theory;
  • Bio mathematics;
  • Symmetry on fractal and fractional differential operators;
  • Data analysis and related topics;
  • Regularity of minimizers for fractional differential equations;
  • Inclusions, inequalities and applications;
  • Stochastic analysis and modeling;
  • Approximation theory and its applications;
  • Disease models via fractional analysis.

Dr. Ahmet Ocak Akdemir
Dr. Zakia Hammouch
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

  • Discrete fractional sums
  • Discrete fractional integral operators
  • Modeling
  • Disease models

Published Papers (4 papers)

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Research

16 pages, 329 KiB  
Article
Some New Bennett–Leindler Type Inequalities via Conformable Fractional Nabla Calculus
by Ghada AlNemer, Mohammed Zakarya, Roqia Butush and Haytham M. Rezk
Symmetry 2022, 14(10), 2183; https://doi.org/10.3390/sym14102183 - 18 Oct 2022
Cited by 1 | Viewed by 965
Abstract
In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of [...] Read more.
In this article, we prove several new fractional nabla Bennett–Leindler dynamic inequalities with the help of a simple consequence of Keller’s chain rule, integration by parts, mean inequalities and Hölder’s inequality for the nabla fractional derivative on time scales. As a result of this, some new classical inequalities are obtained as special cases, and we extended our inequalities to discrete and continuous calculus. In addition, when α=1, we shall obtain some well-known dynamic inequalities as special instances from our results. Symmetrical properties are critical in determining the best ways to solve inequalities. Full article
(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)
16 pages, 302 KiB  
Article
Some Inequalities Related to Jensen-Type Results with Applications
by Imran Abbas Baloch, Aqeel Ahmad Mughal, Absar Ul Haq and Kamsing Nonlaopon
Symmetry 2022, 14(8), 1585; https://doi.org/10.3390/sym14081585 - 2 Aug 2022
Viewed by 1023
Abstract
The class of harmonic convex functions has acquired a very useful and significant placement among the non-convex functions, since this class not only reinforces some major results of the class of convex functions, but also has supported the development of some remarkable results [...] Read more.
The class of harmonic convex functions has acquired a very useful and significant placement among the non-convex functions, since this class not only reinforces some major results of the class of convex functions, but also has supported the development of some remarkable results in analysis where the class of convex functions is silent. Therefore, many researchers have deployed themselves to explore valuable results for this class of non-convex functions. This paper obtains new discrete inequalities for univariate harmonic convex functions on linear spaces related to a Jensen-type and a variant of the Jensen-type results. Our results are refinements of very important recent inequalities presented by Dragomir and Baloch et al. Furthermore, we provide the natural applications of our results. Full article
(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)
20 pages, 428 KiB  
Article
Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative
by Omid Nikan, Ho Duy Binh, Zakieh Avazzadeh and Le Dinh Long
Symmetry 2022, 14(7), 1490; https://doi.org/10.3390/sym14071490 - 21 Jul 2022
Viewed by 1279
Abstract
The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Φ,g)∈L2(0,T)×L2(Ω), we give a [...] Read more.
The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Φ,g)∈L2(0,T)×L2(Ω), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in Lq(D), with q≠2 under some reasonable Cauchy data assumptions. Full article
(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)
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13 pages, 504 KiB  
Article
On a Fractional Parabolic Equation with Regularized Hyper-Bessel Operator and Exponential Nonlinearities
by Dumitru Baleanu, Ho Duy Binh and Anh Tuan Nguyen
Symmetry 2022, 14(7), 1419; https://doi.org/10.3390/sym14071419 - 11 Jul 2022
Cited by 4 | Viewed by 1390
Abstract
Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild [...] Read more.
Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity. Full article
(This article belongs to the Special Issue Symmetry in New Trends for Discrete Fractional Calculus with Applications)
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