On Fuzzy Extended Hexagonal <i>b</i>-Metric Spaces with Applications to Nonlinear Fractional Differential Equations
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...
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| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/bfe8c68ac906427fafc1b74591116c44 |
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| Sumario: | 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. |
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