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Axioms
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Mathematical Analysis and Applications
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Mathematical Analysis and Applications

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

Deadline for manuscript submissions: closed (31 August 2018) | Viewed by 58217

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modeling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.

We look forward to your contributions to this Special Issue,

Best wishes,

Prof. Dr. Hari M. Srivastava
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

  • Mathematical (or Higher Transcendental) Functions and Their Applications
  • Fractional Calculus and Its Applications
  • q-Series and q-Polynomials
  • Analytic Number Theory
  • Special Functions of Mathematical Physics and Applied Mathematics
  • Geometric Function Theory of Complex Analysis

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Published Papers (16 papers)

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Editorial

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2 pages, 158 KiB  
Editorial
Mathematical Analysis and Applications
by Hari M. Srivastava
Axioms 2018, 7(4), 82; https://doi.org/10.3390/axioms7040082 - 12 Nov 2018
Viewed by 2594
Abstract
Website: http://www.math.uvic.ca/faculty/harimsri/ [...] Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)

Research

Jump to: Editorial

10 pages, 233 KiB  
Article
New Bell–Sheffer Polynomial Sets
by Pierpaolo Natalini and Paolo Emilio Ricci
Axioms 2018, 7(4), 71; https://doi.org/10.3390/axioms7040071 - 08 Oct 2018
Cited by 6 | Viewed by 2968
Abstract
In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results [...] Read more.
In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results by Dattoli and Ben Cheikh on the monomiality principle, showing the possibility to derive explicitly the main properties of Sheffer polynomial families starting from the basic elements of their generating functions. The introduction of iterated exponential and logarithmic functions allows to construct new sets of Bell–Sheffer polynomials which exhibit an iterative character of the obtained shift operators and differential equations. In this context, it is possible, for every integer r, to define polynomials of higher type, which are linked to the higher order Bell-exponential and logarithmic numbers introduced in preceding papers. Connections with integer sequences appearing in Combinatorial analysis are also mentioned. Naturally, the considered technique can also be used in similar frameworks, where the iteration of exponential and logarithmic functions appear. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
13 pages, 809 KiB  
Article
Periodically Forced Nonlinear Oscillatory Acoustic Vacuum
by Makrina Agaoglou, Michal Fečkan, Michal Pospíšil, Vassilis M. Rothos and Alexander F. Vakakis
Axioms 2018, 7(4), 69; https://doi.org/10.3390/axioms7040069 - 22 Sep 2018
Cited by 1 | Viewed by 3088
Abstract
In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced system. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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17 pages, 281 KiB  
Article
Solutions to Abel’s Integral Equations in Distributions
by Chenkuan Li, Thomas Humphries and Hunter Plowman
Axioms 2018, 7(3), 66; https://doi.org/10.3390/axioms7030066 - 02 Sep 2018
Cited by 5 | Viewed by 3858
Abstract
The goal of this paper is to study fractional calculus of distributions, the generalized Abel’s integral equations, as well as fractional differential equations in the distributional space D ′ ( R + ) based on inverse convolutional operators and Babenko’s approach. Furthermore, we [...] Read more.
The goal of this paper is to study fractional calculus of distributions, the generalized Abel’s integral equations, as well as fractional differential equations in the distributional space D ′ ( R + ) based on inverse convolutional operators and Babenko’s approach. Furthermore, we provide interesting applications of Abel’s integral equations in viscoelastic systems, as well as solving other integral equations, such as ∫ θ π / 2 y ( φ ) cos β φ ( cos θ − cos φ ) α d φ = f ( θ ) , and ∫ 0 ∞ x 1 / 2 g ( x ) y ( x + t ) d x = f ( t ) . Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
16 pages, 856 KiB  
Article
Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions
by Jean-Daniel Djida and Arran Fernandez
Axioms 2018, 7(3), 65; https://doi.org/10.3390/axioms7030065 - 01 Sep 2018
Cited by 3 | Viewed by 3509
Abstract
The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic equation with mixed Dirichlet–Neumann boundary conditions. The degenerate elliptic equation [...] Read more.
The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic equation with mixed Dirichlet–Neumann boundary conditions. The degenerate elliptic equation arises from the Bernardis–Reyes–Stinga–Torrea extension of the Dirichlet problem for the Marchaud fractional derivative. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
9 pages, 243 KiB  
Article
Umbral Methods and Harmonic Numbers
by Giuseppe Dattoli, Bruna Germano, Silvia Licciardi and Maria Renata Martinelli
Axioms 2018, 7(3), 62; https://doi.org/10.3390/axioms7030062 - 01 Sep 2018
Cited by 5 | Viewed by 3023
Abstract
The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
14 pages, 487 KiB  
Article
Sub-Optimal Control in the Zika Virus Epidemic Model Using Differential Evolution
by Nonthamon Chaikham and Wannika Sawangtong
Axioms 2018, 7(3), 61; https://doi.org/10.3390/axioms7030061 - 23 Aug 2018
Cited by 2 | Viewed by 3261
Abstract
A dynamical model of Zika virus (ZIKV) epidemic with direct transmission, sexual transmission, and vertical transmission is developed. A sub-optimal control problem to counter against the disease is proposed including three controls: vector elimination, vector-to-human contact reduction, and sexual contact reduction. Each control [...] Read more.
A dynamical model of Zika virus (ZIKV) epidemic with direct transmission, sexual transmission, and vertical transmission is developed. A sub-optimal control problem to counter against the disease is proposed including three controls: vector elimination, vector-to-human contact reduction, and sexual contact reduction. Each control variable is discretized into piece-wise constant intervals. The problem is solved by Differential Evolution (DE), which is one of the evolutionary algorithm developed for optimization. Two scenarios, namely four time horizons and eight time horizons, are compared and discussed. The simulations show that models with controls lead to decreasing the number of patients as well as epidemic period length. From the optimal solution, vector elimination is the prioritized strategy for disease control. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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19 pages, 894 KiB  
Article
Some Identities for Euler and Bernoulli Polynomials and Their Zeros
by Taekyun Kim and Cheon Seoung Ryoo
Axioms 2018, 7(3), 56; https://doi.org/10.3390/axioms7030056 - 14 Aug 2018
Cited by 43 | Viewed by 4386 | Correction
Abstract
In this paper, we study some special polynomials which are related to Euler and Bernoulli polynomials. In addition, we give some identities for these polynomials. Finally, we investigate the zeros of these polynomials by using the computer. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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11 pages, 273 KiB  
Article
A New Type of Generalization on W—Asymptotically J λ—Statistical Equivalence with the Number of α
by Hafize Gümüş and Nihal Demir
Axioms 2018, 7(3), 54; https://doi.org/10.3390/axioms7030054 - 02 Aug 2018
Cited by 1 | Viewed by 3037
Abstract
In our paper, by using the concept of W−asymptotically J− statistical equivalence of order α which has been previously defined, we present the definitions of W−asymptotically Jλ−statistical equivalence of order α, W−strongly [...] Read more.
In our paper, by using the concept of W−asymptotically J− statistical equivalence of order α which has been previously defined, we present the definitions of W−asymptotically Jλ−statistical equivalence of order α, W−strongly asymptotically Jλ−statistical equivalence of order α, and W−strongly Cesáro asymptotically J−statistical equivalence of order α where 0<α≤1. We also extend these notions with a sequence of positive real numbers, p=(pk), and we investigate how our results change if p is constant. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
18 pages, 2902 KiB  
Article
Some Exact Solutions to Non-Fourier Heat Equations with Substantial Derivative
by Konstantin Zhukovsky, Dmitrii Oskolkov and Nadezhda Gubina
Axioms 2018, 7(3), 48; https://doi.org/10.3390/axioms7030048 - 18 Jul 2018
Cited by 10 | Viewed by 3685
Abstract
One-dimensional equations of telegrapher’s-type (TE) and Guyer–Krumhansl-type (GK-type) with substantial derivative considered and operational solutions to them are given. The role of the exponential differential operators is discussed. The examples of their action on some initial functions are explored. Proper solutions are constructed [...] Read more.
One-dimensional equations of telegrapher’s-type (TE) and Guyer–Krumhansl-type (GK-type) with substantial derivative considered and operational solutions to them are given. The role of the exponential differential operators is discussed. The examples of their action on some initial functions are explored. Proper solutions are constructed in the integral form and some examples are studied with solutions in elementary functions. A system of hyperbolic-type inhomogeneous differential equations (DE), describing non-Fourier heat transfer with substantial derivative thin films, is considered. Exact harmonic solutions to these equations are obtained for the Cauchy and the Dirichlet conditions. The application to the ballistic heat transport in thin films is studied; the ballistic properties are accounted for by the Knudsen number. Two-speed heat propagation process is demonstrated—fast evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow diffusive heat-exchange process. The comparative analysis of the obtained solutions is performed. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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20 pages, 253 KiB  
Article
Some Summation Theorems for Generalized Hypergeometric Functions
by Mohammad Masjed-Jamei and Wolfram Koepf
Axioms 2018, 7(2), 38; https://doi.org/10.3390/axioms7020038 - 08 Jun 2018
Cited by 11 | Viewed by 4307
Abstract
Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized hypergeometric series in [...] Read more.
Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized hypergeometric series in order to extend some classical summation theorems of hypergeometric functions such as Gauss, Kummer, Dixon, Watson, Whipple, Pfaff–Saalschütz and Dougall formulas and also obtain some new summation theorems in the sequel. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
10 pages, 249 KiB  
Article
Pre-Metric Spaces Along with Different Types of Triangle Inequalities
by Hsien-Chung Wu
Axioms 2018, 7(2), 34; https://doi.org/10.3390/axioms7020034 - 24 May 2018
Cited by 3 | Viewed by 3830
Abstract
The T 1 -spaces induced by the pre-metric spaces along with many forms of triangle inequalities are investigated in this paper. The limits in pre-metric spaces are also studied to demonstrate the consistency of limit concept in the induced topologies. [...] Read more.
The T 1 -spaces induced by the pre-metric spaces along with many forms of triangle inequalities are investigated in this paper. The limits in pre-metric spaces are also studied to demonstrate the consistency of limit concept in the induced topologies. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
13 pages, 281 KiB  
Article
Yukawa Potential, Panharmonic Measure and Brownian Motion
by Antti Rasila and Tommi Sottinen
Axioms 2018, 7(2), 28; https://doi.org/10.3390/axioms7020028 - 01 May 2018
Cited by 3 | Viewed by 4159
Abstract
This paper continues our earlier investigation, where a walk-on-spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs) was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind [...] Read more.
This paper continues our earlier investigation, where a walk-on-spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs) was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure, which is a generalization of the harmonic measure for the Yukawa PDE. We show that there are natural stochastic definitions for the panharmonic measure in terms of the Brownian motion and that the harmonic and the panharmonic measures are all mutually equivalent. Furthermore, we calculate their Radon–Nikodym derivatives explicitly for some balls, which is a key result behind the WOS algorithm. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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13 pages, 316 KiB  
Article
Subordination Properties for Multivalent Functions Associated with a Generalized Fractional Differintegral Operator
by Hanaa M. Zayed, Mohamed Kamal Aouf and Adela O. Mostafa
Axioms 2018, 7(2), 27; https://doi.org/10.3390/axioms7020027 - 24 Apr 2018
Cited by 5 | Viewed by 3541
Abstract
Using of the principle of subordination, we investigate some subordination and convolution properties for classes of multivalent functions under certain assumptions on the parameters involved, which are defined by a generalized fractional differintegral operator under certain assumptions on the parameters involved. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
12 pages, 302 KiB  
Article
New Definitions about A I -Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences
by Ömer Kişi, Hafize Gümüş and Ekrem Savas
Axioms 2018, 7(2), 24; https://doi.org/10.3390/axioms7020024 - 13 Apr 2018
Cited by 3 | Viewed by 4033
Abstract
In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical convergence, which is a recently introduced summability method. The names of our new methods are A I -lacunary statistical [...] Read more.
In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I -statistical convergence, which is a recently introduced summability method. The names of our new methods are A I -lacunary statistical convergence and strongly A I -lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by S θ A I , F and N θ A I , F , respectively. We give some inclusion relations between S A I , F , S θ A I , F and N θ A I , F . We also investigate Cesáro summability for A I and we obtain some basic results between A I -Cesáro summability, strongly A I -Cesáro summability and the spaces mentioned above. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
12 pages, 800 KiB  
Article
Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods
by Yilmaz Simsek
Axioms 2018, 7(2), 22; https://doi.org/10.3390/axioms7020022 - 01 Apr 2018
Cited by 13 | Viewed by 3827
Abstract
In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol-Bernoulli polynomials and numbers of order [...] Read more.
In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol-Bernoulli polynomials and numbers of order k and the Apostol-Euler polynomials and numbers of order k. Moreover, by using p-adic integral technique, we also derive some combinatorial sums including the Bernoulli numbers, the Euler numbers, the Apostol-Euler numbers and the numbers y 1 n , k ; λ . Finally, we make some remarks and observations regarding these identities and relations. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications)
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