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Axioms
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Advances in Applied Mathematical Analysis
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Advances in Applied Mathematical Analysis

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

Deadline for manuscript submissions: closed (30 September 2021) | Viewed by 5805

Special Issue Editor

Prof. Dr. Dimplekumar N. Chalishajar

E-Mail Website
Guest Editor
Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA
Interests: differentiation; applied mathematics; mathematical analysis; functional analysis; nonlinear analysis; differential equations; engineering, applied and computational mathematics; partial differential equations; numerical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, “Advances in Applied Mathematical Analysis”, will publish high-quality mathematical papers on functional differential equations. Emphasis shall be placed on developments in the theory of delay differential, integro-differential, impulsive differential, and difference equations and their applications. Some of the possible topics of the papers invited include, for example, various boundary value problems, positivity/negativity of their solutions, Green’s functions and their properties, existence and uniqueness solutions of nonlinear boundary value problems, optimization and control theory, stability theory, oscillation and non-oscillation, variational problems, and the use of functional differential equations in technology, economics, biology, and medicine.

In interdisciplinary approaches, which necessarily combine concepts and tools from different fields, mathematics is commonly the language used to smartly merge all the different concepts into a unique model. Cross-border modeling and numerical simulation works within the subfields of physics and engineering are particularly welcome in this Special Issue.  

The scope includes (but is not limited to) original research works providing characterizations, explanations, predictions of systems, and phenomena supporting the emergence of potentially novel, useful applications that can even be at a very early stage of conception. Papers based on advances in the theory of stochastic processes and stochastic models are also welcome. The papers devoted to local and nonlocal condition and transference differential equations of heat and mass transference mathematical processes in continuous media with memory and in media with fractal structure will be considered. These papers shall investigate modified initial and mixed boundary value problems for generalized transfer differential equations of integral and fractional orders, and the fields of qualitative and quantitative analysis of nonlinear evolution equations and their applications in image analysis. Both analytical studies as well as simulation-based studies will be considered. We will cover mathematical problems in materials science, mathematical approaches to image processing with applications, applications of partial differential equations, recent advances in delay differential and difference equations, nonlinear optimization, variational inequalities and equilibrium problems, computational methods in analysis and applications, and all applied mathematical fields.

Prof. Dr. Dimplekumar N. Chalishajar
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

  • Functional differential equations/fractional differential equations/dynamical differential equations/partial differential equations
  • Oscillation/non-oscillation
  • Feedback control, controllability, and stability
  • Boundary value problems
  • Markov chain and Jump processes
  • Coupled dynamics
  • Fractional processes, fractional integral
  • Space–time fractional equations
  • Fractional Brownian motion and Rosenblatt process
  • Long-range dependence
  • Time–space fractional vibration equation
  • Biological mathematics and engineering mathematics
  • Numerical simulation

Published Papers (3 papers)

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Research

15 pages, 349 KiB  
Article
New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations
by Aníbal Coronel, Fernando Huancas, Alex Tello and Marko Rojas-Medar
Axioms 2021, 10(3), 205; https://doi.org/10.3390/axioms10030205 - 29 Aug 2021
Cited by 1 | Viewed by 1263
Abstract
We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the [...] Read more.
We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Analysis)
16 pages, 1098 KiB  
Article
Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme
by Hisham M. Almongy, Fatma Y. Alshenawy, Ehab M. Almetwally and Doaa A. Abdo
Axioms 2021, 10(2), 100; https://doi.org/10.3390/axioms10020100 - 21 May 2021
Cited by 27 | Viewed by 2019
Abstract
In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood [...] Read more.
In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Analysis)
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14 pages, 284 KiB  
Article
Controllability of Fuzzy Solutions for Neutral Impulsive Functional Differential Equations with Nonlocal Conditions
by Falguni Acharya, Vandana Kushawaha, Jitendra Panchal and Dimplekumar Chalishajar
Axioms 2021, 10(2), 84; https://doi.org/10.3390/axioms10020084 - 06 May 2021
Cited by 4 | Viewed by 1656
Abstract
In this paper, the controllability of fuzzy solutions for first order nonlocal impulsive neutral functional differential equations is explored using the Banach fixed point theorem. We utilized the concepts of the fuzzy set theory, functional analysis, and the Hausdorff metric. In the conclusion, [...] Read more.
In this paper, the controllability of fuzzy solutions for first order nonlocal impulsive neutral functional differential equations is explored using the Banach fixed point theorem. We utilized the concepts of the fuzzy set theory, functional analysis, and the Hausdorff metric. In the conclusion, an illustration is given to bolster the hypothesis. Full article
(This article belongs to the Special Issue Advances in Applied Mathematical Analysis)
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