Special Issue "Recent Advances in Discrete and Fractional Mathematics"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 30 April 2020.

Special Issue Editors

Prof. Dr. Jose M. Rodriguez
E-Mail Website
Guest Editor
Department of Mathematics, Carlos III University of Madrid-Leganés Campus, Avenida de la Universidad 30, CP-28911, Leganés, Madrid, Spain
Interests: discrete mathematics; fractional calculus; topological indices; polynomials in graphs; geometric function theory; geometry; approximation theory
Special Issues and Collections in MDPI journals
Prof. Dr. José M. Sigarreta
E-Mail Website
Guest Editor
Faculty of Mathematics. Autonomous University of Guerrero-Acapulco Campus, Calle Carlos E. Adame 54, Garita, CP-39650, Acapulco, Guerrero, Mexico
Interests: discrete mathematics; alliances in graphs; conformable and non-conformable calculus; geometry; topological indices

Special Issue Information

Dear Colleagues,

Although Discrete and Fractional Mathematics has always played an important role in Mathematics, in recent years, this role has significantly increased in several branches of these fields, including, but not limited to:

Gromov hyperbolic graphs, domination theory, differential of graphs, polynomials in graphs, alliances in graphs, complex systems, topological indices, discrete geometry, fractional differential equations, fractional integral operators, and discrete and fractional inequalities.

The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results on these topics involving their symmetry properties, both from a theoretical and an applied point of view.

Prof. Dr. Jose M. Rodriguez
Prof. Dr.  José M. Sigarreta
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 papers will be 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 1400 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 Mathematics
  • Graph Theory
  • Hyperbolic Graphs
  • Domination in Graphs
  • Differential of Graphs
  • Polynomials in Graphs
  • Alliances in Graphs
  • Complex Systems
  • Topological Indices
  • Discrete Geometry
  • Fractional Calculus
  • Fractional Differential Equations
  • Fractional Integral Operators
  • Conformable and Non-Conformable Calculus
  • Discrete and Fractional Inequalities

Published Papers (5 papers)

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Research

Open AccessArticle
On the Inverse Degree Polynomial
Symmetry 2019, 11(12), 1490; https://doi.org/10.3390/sym11121490 - 07 Dec 2019
Abstract
Using the symmetry property of the inverse degree index, in this paper, we obtain several mathematical relations of the inverse degree polynomial, and we show that some properties of graphs, such as the cardinality of the set of vertices and edges, or the [...] Read more.
Using the symmetry property of the inverse degree index, in this paper, we obtain several mathematical relations of the inverse degree polynomial, and we show that some properties of graphs, such as the cardinality of the set of vertices and edges, or the cyclomatic number, can be deduced from their inverse degree polynomials. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
Open AccessArticle
Improved Image Splicing Forgery Detection by Combination of Conformable Focus Measures and Focus Measure Operators Applied on Obtained Redundant Discrete Wavelet Transform Coefficients
Symmetry 2019, 11(11), 1392; https://doi.org/10.3390/sym11111392 - 10 Nov 2019
Abstract
The image is the best information carrier in the current digital era and the easiest to manipulate. Image manipulation causes the integrity of this information carrier to be ambiguous. The image splicing technique is commonly used to manipulate images by fusing different regions [...] Read more.
The image is the best information carrier in the current digital era and the easiest to manipulate. Image manipulation causes the integrity of this information carrier to be ambiguous. The image splicing technique is commonly used to manipulate images by fusing different regions in one image. Over the last decade, it has been confirmed that various structures in science and engineering can be demonstrated more precisely by fractional calculus using integrals or derivative operators. Many fractional-order-based techniques have been used in the image-processing field. Recently, a new specific fractional calculus, called conformable calculus, was delivered. Herein, we employ the combination of conformable focus measures (CFMs), and focus measure operators (FMOs) in obtaining redundant discrete wavelet transform (RDWT) coefficients for improving the image splicing forgery detection. The process of image splicing disorders the content of tampered image and causes abnormality in the image features. The spliced region’s boundaries are usually blurring to avoid detection. To make use of the blurred information, both CFMs and FMOs are used to calculate the degree of blurring of the tampered region’s boundaries for image splicing detection. The two public image datasets IFS-TC and CASIA TIDE V2 are used for evaluation of the proposed method. The obtained results of the proposed method achieved accuracy rate 98.30% for Cb channel on IFS-TC image dataset and 98.60% of the Cb channel on CASIA TIDE V2 with 24-D feature vector. The proposed method exhibited superior results compared with other image splicing detection methods. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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Open AccessArticle
A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model
Symmetry 2019, 11(11), 1330; https://doi.org/10.3390/sym11111330 - 24 Oct 2019
Abstract
In this work, we propose an efficient multi-stage homotopy perturbation method to find an analytic solution to the fractional Lotka-Volterra model. We obtain its order of accuracy, and we study the stability of the system. Moreover, we present several examples to show of [...] Read more.
In this work, we propose an efficient multi-stage homotopy perturbation method to find an analytic solution to the fractional Lotka-Volterra model. We obtain its order of accuracy, and we study the stability of the system. Moreover, we present several examples to show of the effectiveness of this method, and we conclude that the value of the derivative order plays an important role in the trajectories velocity. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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Open AccessFeature PaperArticle
A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework
Symmetry 2019, 11(10), 1322; https://doi.org/10.3390/sym11101322 - 22 Oct 2019
Abstract
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due [...] Read more.
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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Open AccessArticle
New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators
Symmetry 2019, 11(9), 1108; https://doi.org/10.3390/sym11091108 - 03 Sep 2019
Cited by 1
Abstract
At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via [...] Read more.
At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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