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Fractal Fract
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Nonlinear Functional Analysis and Applications
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Nonlinear Functional Analysis and Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 January 2023) | Viewed by 3681

Special Issue Editor

Dr. Ji Eun Kim

E-Mail Website
Guest Editor
Department of Mathematics, Dongguk University, Gyeongju-si 38066, Republic of Korea
Interests: calculus; quaternion analysis; Clifford analysis; mathematical physics; computational methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue titled “Nonlinear Functional Analysis and Applications” provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This Special Issue provides an introduction to the basic concepts and techniques of this field. This Special Issue provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. This Special Issue considers the various settings in nonlinear functional analysis in which differentials play a significant role. This Special Issue also discusses the generalized inverse for a bounded linear operator, whose range is not necessarily closed. This Special Issue also deals with the analogous Cauchy–Riemann equations for extended quaternions and Clifford algebras, which consist of differential operators and derivatives. Authors who are interested in nonlinear functional analysis and quaternion analysis will also find this Special Issue useful.

Potential topics include, but are not limited to:

  • nonlinear functional analysis;
  • Cauchy–Riemann equations;
  • quaternion analysis;
  • differential operators;
  • PDE.

This special issue considers the various settings in nonlinear functional analysis in which differentials play a significant role. This special issue discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. This special issue also deals with the analogous Cauchy-Riemann equations for extended quaternions and Clifford algebras, which consist of differential operators and derivatives. This special issue provides an introduction to the basic concepts and techniques of nonlinear functional analysis.

Prof. Dr. Ji Eun Kim
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at mdpi.longhoe.net 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. Fractal and Fractional 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 2700 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

  • nonlinear functional analysis
  • Cauchy-Riemann equations
  • quaternion analysis
  • differential operators
  • PDE

Published Papers (3 papers)

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Research

18 pages, 1228 KiB  
Article
On the Bilinear Second Order Differential Realization of an Infinite-Dimensional Dynamical System: An Approach Based on Extensions to M2-Operators
by V. A. Rusanov, A. V. Lakeyev, A. V. Banshchikov and A. V. Daneev
Fractal Fract. 2023, 7(4), 310; https://doi.org/10.3390/fractalfract7040310 - 3 Apr 2023
Cited by 2 | Viewed by 881
Abstract
Considering the case of a continual bundle of controlled dynamic processes, the authors have studied the functional-geometric conditions of existence of non-stationary coefficients-operators from the differential realization of this bundle in the class of non-autonomous bilinear second-order differential equations in the separable Hilbert [...] Read more.
Considering the case of a continual bundle of controlled dynamic processes, the authors have studied the functional-geometric conditions of existence of non-stationary coefficients-operators from the differential realization of this bundle in the class of non-autonomous bilinear second-order differential equations in the separable Hilbert space. The problem under scrutiny belongs to the type of non-stationary coefficient-operator inverse problems for the bilinear evolution equations in the Hilbert space. The solution is constructed on the basis of usage of the functional Relay-Ritz operator. Under this mathematical problem statement, the case has been studied in detail when the operators to be modeled are burdened with the condition, which provides for entire continuity of the integral representation equations of the model of realization. Proposed is the entropy interpretation of the given problem of mathematical modeling of continual bundle dynamic processes in the context of development of the qualitative theory of differential realization of nonlinear state equations of complex infinite-dimensional behavioristic dynamical system. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Applications)
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20 pages, 3919 KiB  
Article
A Nonlinear Fractional BEM Model for Magneto-Thermo-Visco-Elastic Ultrasound Waves in Temperature-Dependent FGA Rotating Granular Plates
by Mohamed Abdelsabour Fahmy
Fractal Fract. 2023, 7(3), 214; https://doi.org/10.3390/fractalfract7030214 - 24 Feb 2023
Cited by 3 | Viewed by 1014
Abstract
The primary goal of this study is to create a nonlinear fractional boundary element method (BEM) model for magneto-thermo-visco-elastic ultrasound wave problems in temperature-dependent functionally graded anisotropic (FGA) rotating granular plates in a constant primary magnetic field. Classical analytical methods are frequently insufficient [...] Read more.
The primary goal of this study is to create a nonlinear fractional boundary element method (BEM) model for magneto-thermo-visco-elastic ultrasound wave problems in temperature-dependent functionally graded anisotropic (FGA) rotating granular plates in a constant primary magnetic field. Classical analytical methods are frequently insufficient to solve the governing equation system of such problems due to nonlinearity, fractional order heat conduction, and strong anisotropy of mechanical properties. To address this challenge, a BEM-based coupling scheme that is both reliable and efficient was proposed, with the Cartesian transformation method (CTM) used to compute domain integrals and the generalized modified shift-splitting (GMSS) method was used to solve the BEM-derived linear systems. The calculation results are graphed to show the effects of temperature dependence, anisotropy, graded parameter, and fractional parameter on nonlinear thermal stress in the investigated plates. The numerical results validate the consistency and effectiveness of the developed modeling methodology. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Applications)
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12 pages, 309 KiB  
Article
Certain Sharp Coefficient Results on a Subclass of Starlike Functions Defined by the Quotient of Analytic Functions
by Lei Shi and Muhammad Arif
Fractal Fract. 2023, 7(2), 195; https://doi.org/10.3390/fractalfract7020195 - 15 Feb 2023
Cited by 3 | Viewed by 1149
Abstract
In the present paper, we consider a subclass of starlike functions G3/2 defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the bounds of Fekete–Szegö-type inequalities and Hankel determinants for functions [...] Read more.
In the present paper, we consider a subclass of starlike functions G3/2 defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the bounds of Fekete–Szegö-type inequalities and Hankel determinants for functions in this class. It is proved that maxH3,1(f):f∈G3/2 is equal to 181. The bounds for f∈G3/2 are sharp. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Applications)
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