On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive...

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Autores principales:	Sumaiya Tasneem Zubair, Kalpana Gopalan, Thabet Abdeljawad, Bahaaeldin Abdalla
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fuzzy extended hexagonal <i>b</i>-metric spaces fixed points nonlinear fractional differential equation of the Caputo type Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bfe8c68ac906427fafc1b74591116c44
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spelling	oai:doaj.org-article:bfe8c68ac906427fafc1b74591116c442021-11-25T19:06:11ZOn Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations10.3390/sym131120322073-8994https://doaj.org/article/bfe8c68ac906427fafc1b74591116c442021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2032https://doaj.org/toc/2073-8994The focus of this research article is to investigate the notion of fuzzy extended hexagonal <i>b</i>-metric spaces as a technique of broadening the fuzzy rectangular <i>b</i>-metric spaces and extended fuzzy rectangular <i>b</i>-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal <i>b</i>-metric spaces is specified as follows utilizing the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></semantics></math></inline-formula>: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>t</mi><mo>+</mo><mi>s</mi><mo>+</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>+</mo><mi>w</mi></mfenced><mo>≥</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>c</mi><mo>,</mo><mi>e</mi><mo>,</mo><mfrac><mi>t</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mfrac><mi>s</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mfrac><mi>u</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>g</mi><mo>,</mo><mi>k</mi><mo>,</mo><mfrac><mi>v</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>k</mi><mo>,</mo><mi>d</mi><mo>,</mo><mfrac><mi>w</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced></mrow></semantics></math></inline-formula> for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mi>e</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>e</mi><mo>≠</mo><mi>f</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>f</mi><mo>≠</mo><mi>g</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>g</mi><mo>≠</mo><mi>k</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>k</mi><mo>≠</mo><mi>d</mi></mrow></semantics></math></inline-formula>. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.Sumaiya Tasneem ZubairKalpana GopalanThabet AbdeljawadBahaaeldin AbdallaMDPI AGarticlefuzzy extended hexagonal <i>b</i>-metric spacesfixed pointsnonlinear fractional differential equation of the Caputo typeMathematicsQA1-939ENSymmetry, Vol 13, Iss 2032, p 2032 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fuzzy extended hexagonal <i>b</i>-metric spaces fixed points nonlinear fractional differential equation of the Caputo type Mathematics QA1-939
spellingShingle	fuzzy extended hexagonal <i>b</i>-metric spaces fixed points nonlinear fractional differential equation of the Caputo type Mathematics QA1-939 Sumaiya Tasneem Zubair Kalpana Gopalan Thabet Abdeljawad Bahaaeldin Abdalla On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
description	The focus of this research article is to investigate the notion of fuzzy extended hexagonal <i>b</i>-metric spaces as a technique of broadening the fuzzy rectangular <i>b</i>-metric spaces and extended fuzzy rectangular <i>b</i>-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal <i>b</i>-metric spaces is specified as follows utilizing the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></semantics></math></inline-formula>: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>c</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>t</mi><mo>+</mo><mi>s</mi><mo>+</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>+</mo><mi>w</mi></mfenced><mo>≥</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>c</mi><mo>,</mo><mi>e</mi><mo>,</mo><mfrac><mi>t</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mfrac><mi>s</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>f</mi><mo>,</mo><mi>g</mi><mo>,</mo><mfrac><mi>u</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>g</mi><mo>,</mo><mi>k</mi><mo>,</mo><mfrac><mi>v</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced><mo>∗</mo><msub><mi mathvariant="fraktur">m</mi><mi mathvariant="sans-serif">h</mi></msub><mfenced separators="" open="(" close=")"><mi>k</mi><mo>,</mo><mi>d</mi><mo>,</mo><mfrac><mi>w</mi><mrow><mi>b</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></mfrac></mfenced></mrow></semantics></math></inline-formula> for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mi>e</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>e</mi><mo>≠</mo><mi>f</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>f</mi><mo>≠</mo><mi>g</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>g</mi><mo>≠</mo><mi>k</mi><mo>,</mo><mspace width="0.277778em"></mspace><mi>k</mi><mo>≠</mo><mi>d</mi></mrow></semantics></math></inline-formula>. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.
format	article
author	Sumaiya Tasneem Zubair Kalpana Gopalan Thabet Abdeljawad Bahaaeldin Abdalla
author_facet	Sumaiya Tasneem Zubair Kalpana Gopalan Thabet Abdeljawad Bahaaeldin Abdalla
author_sort	Sumaiya Tasneem Zubair
title	On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
title_short	On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
title_full	On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
title_fullStr	On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
title_full_unstemmed	On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
title_sort	on fuzzy extended hexagonal <i>b</i>-metric spaces with applications to nonlinear fractional differential equations
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bfe8c68ac906427fafc1b74591116c44
work_keys_str_mv	AT sumaiyatasneemzubair onfuzzyextendedhexagonalibimetricspaceswithapplicationstononlinearfractionaldifferentialequations AT kalpanagopalan onfuzzyextendedhexagonalibimetricspaceswithapplicationstononlinearfractionaldifferentialequations AT thabetabdeljawad onfuzzyextendedhexagonalibimetricspaceswithapplicationstononlinearfractionaldifferentialequations AT bahaaeldinabdalla onfuzzyextendedhexagonalibimetricspaceswithapplicationstononlinearfractionaldifferentialequations
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On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

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