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Axioms
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Special Functions and Their Applications
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Special Functions and Their Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 14862

Special Issue Editor

Prof. Dr. Clemente Cesarano

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,

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 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.

Keywords

  • Special functions
  • Orthogonal polynomials
  • Generating functions

Published Papers (6 papers)

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Research

17 pages, 783 KiB  
Article
Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions
by Miguel Vivas-Cortez, Artion Kashuri, Rozana Liko and Jorge Eliecer Hernández Hernández
Axioms 2020, 9(4), 117; https://doi.org/10.3390/axioms9040117 - 15 Oct 2020
Cited by 5 | Viewed by 1874
Abstract
In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions [...] Read more.
In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well. Full article
(This article belongs to the Special Issue Special Functions and Their Applications)
14 pages, 374 KiB  
Article
Approximating Functions of Positive Compact Operators by Using Bell Polynomials
by Diego Caratelli, Pierpaolo Natalini and Paolo Emilio Ricci
Axioms 2020, 9(3), 73; https://doi.org/10.3390/axioms9030073 - 30 Jun 2020
Viewed by 1467
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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14 pages, 302 KiB  
Article
Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions
by Miguel J. Vivas-Cortez, Artion Kashuri, Rozana Liko and Jorge E. Hernández
Axioms 2020, 9(1), 12; https://doi.org/10.3390/axioms9010012 - 26 Jan 2020
Cited by 17 | Viewed by 2174
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)
9 pages, 252 KiB  
Article
A Versatile Integral in Physics and Astronomy and Fox’s H-Function
by Arak M. Mathai and Hans J. Haubold
Axioms 2019, 8(4), 122; https://doi.org/10.3390/axioms8040122 - 01 Nov 2019
Cited by 3 | Viewed by 2173
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)
11 pages, 1150 KiB  
Article
An Efficient Class of Traub–Steffensen-Type Methods for Computing Multiple Zeros
by Deepak Kumar, Janak Raj Sharma and Clemente Cesarano
Axioms 2019, 8(2), 65; https://doi.org/10.3390/axioms8020065 - 25 May 2019
Cited by 8 | Viewed by 2888
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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7 pages, 253 KiB  
Article
Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay
by Clemente Cesarano and Omar Bazighifan
Axioms 2019, 8(2), 61; https://doi.org/10.3390/axioms8020061 - 18 May 2019
Cited by 34 | Viewed by 3206
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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