Special Issue "Mathematical Analysis and Applications III"

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

Deadline for manuscript submissions: 31 December 2022 | Viewed by 1807

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 modelling and optimization
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Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issues “Mathematical Analysis and Applications” and “Mathematical Analysis and Applications II”.

Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. As in the abovementioned successful Special Issues, in this Special Issue, we invite and welcome review, expository and original research articles dealing with recent advances in mathematical analysis and its multidisciplinary applications.

We look forward to your contributions to this Special Issue.

Prof. Dr. Hari Mohan 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 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

  • 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 (2 papers)

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Research

Article
Optimal Mittag–Leffler Summation
Axioms 2022, 11(5), 202; https://doi.org/10.3390/axioms11050202 - 24 Apr 2022
Viewed by 806
Abstract
A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes for variables tending to infinity. The method is developed in two versions, as the self-similar Borel–Leroy or Mittag–Leffler summations. It is based on [...] Read more.
A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes for variables tending to infinity. The method is developed in two versions, as the self-similar Borel–Leroy or Mittag–Leffler summations. It is based on optimized self-similar iterated roots approximants applied to the Borel–Leroy and Mittag–Leffler- transformed series with the subsequent inverse transformations. As a result, simple and transparent expressions for the critical amplitudes are obtained in explicit form. The control parameters come into play from the Borel–Leroy and Mittag–Leffler transformations. They are determined from the optimization procedure, either from the minimal derivative or minimal difference conditions, imposed on the analytically expressed critical amplitudes. After diff-log transformation, virtually the same procedure can be applied to critical indices at infinity. The results are obtained for a number of various examples. The examples vary from a rapid growth of the coefficients to a fast decay, as well as intermediate cases. The methods give good estimates for the large-variable critical amplitudes and exponents. The Mittag–Leffler summation works uniformly well for a wider variety of examples. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications III)
Article
An Effective Approximation Algorithm for Second-Order Singular Functional Differential Equations
Axioms 2022, 11(3), 133; https://doi.org/10.3390/axioms11030133 - 14 Mar 2022
Viewed by 655
Abstract
In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system [...] Read more.
In this research study, a novel computational algorithm for solving a second-order singular functional differential equation as a generalization of the well-known Lane–Emden and differential-difference equations is presented by using the Bessel bases. This technique depends on transforming the problem into a system of algebraic equations and by solving this system the unknown Bessel coefficients are determined and the solution will be known. The method is tested on several test examples and proves to provide accurate results as compared to other existing methods from the literature. The simplicity and robustness of the proposed technique drive us to investigate more of their applications to several similar problems in the future. Full article
(This article belongs to the Special Issue Mathematical Analysis and Applications III)
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