Non-local Mathematical Models and Applications: A Theme Issue in Honor of Prof. Carlo Cattani

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 6073

Special Issue Editor


E-Mail Website
Guest Editor
Section of Mathematics, International Telematic University, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Interests: special functions; orthogonal polynomials; differential equations; operator theory; multivariate approximation theory; Lie algebra
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical models originate from concrete questions that arise in the industrial, economic, medical, biological, etc. and are often formulated using functional equations of various types, such as differential, integrodifferential, difference equations and in particular, for non-local aspects, differential equations with fractional operators. One of the fundamental problems in the approach to the numerical solution of such equations is the reconstruction of functions in one or more dimensions, as well as concrete problems starting from a robust theoretical foundation, and developing efficient methods and algorithms implementable, up to the construction of dedicated software. At the base of the various application models, and in this sense the cornerstone from which they express themselves and where many lines of research are founded, is precisely the Theory of Approximation.

The Special Issue is honoring Prof. Carlo Cattani (Habil. Full Professor, since 2017), Professor of Mathematical Physics and Applied Mathematics at the Department of Economics, Engineering, Society and Enterprise (DEIM) of Tuscia University (VT), Italy, since 2015. He was previously appointed as professor/research fellow at the Dept. of Mathematics of University of Rome “La Sapienza” (1980–2004) and Dept. of Mathematics, University of Salerno (2004–2015). He was a Research Fellow at the Italian Council of Research, CNR, in 1978–1980 and Visiting Research Fellow at the Physics Institute of the Stockholm University (1987–1988). His main scientific research interests are numerical and computational methods, mathematical models and methods, time series and data analysis, and computer methods and simulations. He is the author of more than 270 scientific papers on international journals and co-author of several books. He has made significant contributions to fundamental topics such as numerical methods, dynamical systems, fractional calculus, fractals, wavelets, nonlinear waves, and data analysis. He is the Editor-in-Chief of the journals Fractal and Fractional and Information Sciences Letters and is also serving as Editor at Several International Scientific Journals. He was awarded Honorary Professor at the Azerbaijan University (2019) and at the BSP University, Ufa-Russia (2009) for “his contribution in research and international cooperation”, and (in 2018) as adjunct Professor at the Ton Duc Thang University—HCMC Vietnam. For his many achievements in research (H-index: Scopus (41), WoS (36), Google Scholar (47)), he was listed in the 2020 World Ranking of Scientists (Top 2%), ranking 85th (3d in Italy) for numerical and computational mathematics, and 16th over 335 Italian mathematicians of this list.

Prof. Dr. Clemente Cesarano
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. Axioms 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.

Published Papers (3 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

22 pages, 388 KiB  
Article
Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems
by Valery Y. Glizer
Axioms 2021, 10(4), 325; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10040325 - 30 Nov 2021
Cited by 3 | Viewed by 1705
Abstract
In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically [...] Read more.
In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented. Full article
22 pages, 1268 KiB  
Article
Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions
by Tamara Antonova, Roman Dmytryshyn and Serhii Sharyn
Axioms 2021, 10(4), 310; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10040310 - 19 Nov 2021
Cited by 9 | Viewed by 1616
Abstract
The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional generalizations—branched continued fraction expansions. We used [...] Read more.
The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional generalizations—branched continued fraction expansions. We used combinations of three- and four-term recurrence relations of the generalized hypergeometric function 3F2 to construct the branched continued fraction expansions of the ratios of this function. We also used the concept of correspondence and the research method to extend convergence, already known for a small region, to a larger region. As a result, we have established some convergence criteria for the expansions mentioned above. It is proved that the branched continued fraction expansions converges to the functions that are an analytic continuation of the ratios mentioned above in some region. The constructed expansions can approximate the solutions of certain differential equations and analytic functions, which are represented by generalized hypergeometric function 3F2. To illustrate this, we have given a few numerical experiments at the end. Full article
Show Figures

Figure 1

8 pages, 259 KiB  
Article
Oscillation and Asymptotic Properties of Differential Equations of Third-Order
by R. Elayaraja, V. Ganesan, Omar Bazighifan and Clemente Cesarano
Axioms 2021, 10(3), 192; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10030192 - 18 Aug 2021
Cited by 4 | Viewed by 1477
Abstract
The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator [...] Read more.
The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ιτ))]β)+cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ιι0 and w(ι):=x(ι)+p(ι)x(ιτ). New oscillation results are established by using the generalized Riccati technique under the assumption of ι0ιa1/β(s)ds<ι0ι1b(s)ds=asι. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem. Full article
Back to TopTop