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Axioms
Special Issues
Trends in Fixed Point Theory and Fractional Calculus
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Trends in Fixed Point Theory and Fractional Calculus

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

Deadline for manuscript submissions: 20 January 2025 | Viewed by 4695

Special Issue Editors

Prof. Dr. Boško Damjanović

E-Mail Website
Guest Editor
Department of Mathematics, University Union—Nikola Tesla, 11158 Belgrade, Serbia
Interests: real analysis; integration; mapping; analysis; real and complex analysis; topology; mathematical analysis; functional analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Pradip Debnath

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Tezpur University, Assam 784028, India
Interests: functional analysis; fixed point theory and fractional calculus; fuzzy mathematics; geographic information system; mathematical statistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus and fixed point theory are the two interrelated disciplines of modern mathematics which have emerged as indispensable tools in the modeling of diverse processes in engineering and physical sciences. These techniques and tools are multidisciplinary in nature and have widespread applications in the study of physical systems. Differential equations, integral equations, wavelet analysis, optimization, and approximation theory are just a few examples that extensively utilize these two topics. The increased complexity in physical phenomena and engineering experiments continually seeks the advancement of these analytic tools in terms of fractional calculus and fixed point theory.

This Special Issue will collect new research findings of the highest quality with novel and illustrative examples and a long-lasting impact on the existing literature to further advance progress in fractional calculus and fixed point theory.

Prof. Dr. Boško Damjanović
Dr. Pradip Debnath
Guest Editors

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

  • fractional calculus
  • functional analysis
  • fixed points
  • nonlinear operator theory
  • variational inequalities
  • numerical analysis and algorithms
  • functional equations and stability
  • ordinary and partial differential equations
  • integral equations
  • calculus of variation
  • wavelet analysis
  • computational fluid dynamics

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Published Papers (7 papers)

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Research

10 pages, 275 KiB  
Article
Fixed-Point Results of F-Contractions in Bipolar p-Metric Spaces
by Nabanita Konwar and Pradip Debnath
Axioms 2024, 13(11), 773; https://doi.org/10.3390/axioms13110773 - 8 Nov 2024
Viewed by 322
Abstract
In this paper, we present new findings on F-contraction in bipolar p-metric spaces. We establish a covariant Banach-type fixed-point theorem and a contravariant Reich-type fixed-point theorem based on F-contraction in these spaces. Additionally, we include an example that demonstrates the [...] Read more.
In this paper, we present new findings on F-contraction in bipolar p-metric spaces. We establish a covariant Banach-type fixed-point theorem and a contravariant Reich-type fixed-point theorem based on F-contraction in these spaces. Additionally, we include an example that demonstrates the applicability of our results. Our results non-trivially extend this covariant Banach-type fixed-point theorem and contravariant Reich type theorem via the concept of F-contraction. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
13 pages, 292 KiB  
Article
Fixed Point Results in Modular b-Metric-like Spaces with an Application
by Nizamettin Ufuk Bostan and Banu Pazar Varol
Axioms 2024, 13(10), 726; https://doi.org/10.3390/axioms13100726 - 18 Oct 2024
Viewed by 501
Abstract
In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and uniqueness of fixed points in [...] Read more.
In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of ξ-convergence, ξ-Cauchy sequence, ξ-completeness and ξ-contraction. The existence and uniqueness of fixed points in the modular b-metric-like space are handled. Moreover, we give some examples and an application to an integral equation to illustrate the usability of the obtained results. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
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20 pages, 332 KiB  
Article
Enriched Z-Contractions and Fixed-Point Results with Applications to IFS
by Ibrahim Alraddadi, Muhammad Din, Umar Ishtiaq, Mohammad Akram and Ioannis K. Argyros
Axioms 2024, 13(8), 562; https://doi.org/10.3390/axioms13080562 - 19 Aug 2024
Viewed by 562
Abstract
In this manuscript, we initiate a large class of enriched (d,Z)-Z-contractions defined on Banach spaces and prove the existence and uniqueness of the fixed point of these contractions. We also provide an example to support our [...] Read more.
In this manuscript, we initiate a large class of enriched (d,Z)-Z-contractions defined on Banach spaces and prove the existence and uniqueness of the fixed point of these contractions. We also provide an example to support our results and give an existence condition for the uniqueness of the solution to the integral equation. The results provided in the manuscript extend, generalize, and modify the existence results. Our research introduces novel fixed-point results under various contractive conditions. Furthermore, we discuss the iterated function system associated with enriched (d,Z)-Z-contractions in Banach spaces and define the enriched Z-Hutchinson operator. A result regarding the convergence of Krasnoselskii’s iteration method and the uniqueness of the attractor via enriched (d,Z)-Z-contractions is also established. Our discoveries not only confirm but also significantly build upon and broaden several established findings in the current body of literature. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
12 pages, 327 KiB  
Article
Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations
by Doaa Filali, Mohammad Dilshad and Mohammad Akram
Axioms 2024, 13(7), 477; https://doi.org/10.3390/axioms13070477 - 16 Jul 2024
Viewed by 589
Abstract
After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The [...] Read more.
After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
17 pages, 312 KiB  
Article
Stability of Fixed Points of Partial Contractivities and Fractal Surfaces
by María A. Navascués
Axioms 2024, 13(7), 474; https://doi.org/10.3390/axioms13070474 - 13 Jul 2024
Viewed by 655
Abstract
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations [...] Read more.
In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
14 pages, 255 KiB  
Article
Three Existence Results in the Fixed Point Theory
by Alexander J. Zaslavski
Axioms 2024, 13(7), 425; https://doi.org/10.3390/axioms13070425 - 25 Jun 2024
Viewed by 834
Abstract
In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
21 pages, 320 KiB  
Article
Fixed-Point Results of Generalized (ϕ,Ψ)-Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations
by Mohammad Akram, Salha Alshaikey, Umar Ishtiaq, Muhammad Farhan, Ioannis K. Argyros and Samundra Regmi
Axioms 2024, 13(6), 415; https://doi.org/10.3390/axioms13060415 - 20 Jun 2024
Viewed by 592
Abstract
In this manuscript, we prove numerous results concerning fixed points, common fixed points, coincidence points, coupled coincidence points, and coupled common fixed points for (ϕ,Ψ)-contractive mappings in the framework of partially ordered controlled metric spaces. Our findings introduce [...] Read more.
In this manuscript, we prove numerous results concerning fixed points, common fixed points, coincidence points, coupled coincidence points, and coupled common fixed points for (ϕ,Ψ)-contractive mappings in the framework of partially ordered controlled metric spaces. Our findings introduce a novel perspective on this mathematical context, and we illustrate the uniqueness of our findings through various explanatory examples. Also, we apply the main result to find the existence and uniqueness of the solution of the system of integral equations as an application. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
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