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 853

Special Issue Editors


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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
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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

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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

Published Papers (2 papers)

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Research

14 pages, 252 KiB  
Article
Three Existence Results in the Fixed Point Theory
by Alexander J. Zaslavski
Axioms 2024, 13(7), 425; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070425 - 25 Jun 2024
Viewed by 458
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://0-doi-org.brum.beds.ac.uk/10.3390/axioms13060415 - 20 Jun 2024
Viewed by 224
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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