Special Issue "Special Functions and Their Applications"

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

Deadline for manuscript submissions: 31 January 2021.

Special Issue Editor

Prof. Dr. Clemente Cesarano
Website SciProfiles
Guest Editor

Special Issue Information

Dear Colleagues,

The theory of generalized special functions is applied in different branches of pure and applied mathematics and physics. A combination of techniques involving methods of algebraic nature and special functions of standard or generalized forms may offer a powerful tool to solve problems in pure and applied mathematics. In this Special Issue, we will cover different topics in pure mathematics, physics, and statistics, in which the combined use of operational methods and special functions has provided solutions that are hardly achievable with conventional means.

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 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. Axioms is an international peer-reviewed open access quarterly 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 1000 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

  • Special functions
  • Orthogonal polynomials
  • Generating functions

Published Papers (5 papers)

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Research

Open AccessArticle
Approximating Functions of Positive Compact Operators by Using Bell Polynomials
Axioms 2020, 9(3), 73; https://doi.org/10.3390/axioms9030073 - 30 Jun 2020
Abstract
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value [...] Read more.
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
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Open AccessArticle
Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions
Axioms 2020, 9(1), 12; https://doi.org/10.3390/axioms9010012 - 26 Jan 2020
Cited by 2
Abstract
In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found [...] Read more.
In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
Open AccessArticle
A Versatile Integral in Physics and Astronomy and Fox’s H-Function
Axioms 2019, 8(4), 122; https://doi.org/10.3390/axioms8040122 - 01 Nov 2019
Cited by 1
Abstract
This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, [...] Read more.
This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Krätzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck–Cohen superstatistics in statistical mechanics, and Mathai’s pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox’s H-function are pointed out. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
Open AccessArticle
An Efficient Class of Traub–Steffensen-Type Methods for Computing Multiple Zeros
Axioms 2019, 8(2), 65; https://doi.org/10.3390/axioms8020065 - 25 May 2019
Cited by 3
Abstract
Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that [...] Read more.
Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that require only evaluations of three functions per iteration. Convergence of the proposed class is demonstrated by means of using a graphical tool, namely basins of attraction. Applicability of the methods is demonstrated through numerical experimentation on different functions that illustrates the efficient behavior. Comparison of numerical results shows that the presented iterative methods are good competitors to the existing techniques. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
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Open AccessArticle
Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay
Axioms 2019, 8(2), 61; https://doi.org/10.3390/axioms8020061 - 18 May 2019
Cited by 20
Abstract
In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential [...] Read more.
In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
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