An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space
In this paper, we first introduce a new family of functions like an implicit function called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>...
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2831 |
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| author | Uma Devi Patel Stojan Radenović |
| author_facet | Uma Devi Patel Stojan Radenović |
| author_sort | Uma Devi Patel |
| collection | DOAJ |
| description | In this paper, we first introduce a new family of functions like an implicit function called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-functions. Furthermore, we introduce a new concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mi>F</mi></mrow></semantics></math></inline-formula>-fuzzy contractive mappings, which is weaker than the class of fuzzy <i>F</i>-contractive mappings. Then, the existence and uniqueness of the fixed point are established for a new type of fuzzy contractive mappings in the setting of fuzzy metric spaces. Moreover, some examples and an application to nonlinear fractional differential equation are given, and these show the importance of the introduced theorems in fuzzy settings. |
| first_indexed | 2024-03-09T13:01:11Z |
| format | Article |
| id | doaj.art-d04c511521764838915c21bb7aa884a5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:01:11Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d04c511521764838915c21bb7aa884a52023-11-30T21:54:18ZengMDPI AGMathematics2227-73902022-08-011016283110.3390/math10162831An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric SpaceUma Devi Patel0Stojan Radenović1Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur 495009, IndiaFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, SerbiaIn this paper, we first introduce a new family of functions like an implicit function called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Γ</mo></semantics></math></inline-formula>-functions. Furthermore, we introduce a new concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Γ</mo><mi>F</mi></mrow></semantics></math></inline-formula>-fuzzy contractive mappings, which is weaker than the class of fuzzy <i>F</i>-contractive mappings. Then, the existence and uniqueness of the fixed point are established for a new type of fuzzy contractive mappings in the setting of fuzzy metric spaces. Moreover, some examples and an application to nonlinear fractional differential equation are given, and these show the importance of the introduced theorems in fuzzy settings.https://www.mdpi.com/2227-7390/10/16/2831fixed points<i>α</i>-<i>η</i>-Γ<i>F</i>-fuzzy contractive map<i>α</i>-Γ<i>F</i>-fuzzy contractive map<i>α</i>-admissiblenonlinear fractional differential equationfuzzy metric space |
| spellingShingle | Uma Devi Patel Stojan Radenović An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space Mathematics fixed points <i>α</i>-<i>η</i>-Γ<i>F</i>-fuzzy contractive map <i>α</i>-Γ<i>F</i>-fuzzy contractive map <i>α</i>-admissible nonlinear fractional differential equation fuzzy metric space |
| title | An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space |
| title_full | An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space |
| title_fullStr | An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space |
| title_full_unstemmed | An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space |
| title_short | An Application to Nonlinear Fractional Differential Equation via <i>α</i>-Γ<i>F</i>-Fuzzy Contractive Mappings in a Fuzzy Metric Space |
| title_sort | application to nonlinear fractional differential equation via i α i γ i f i fuzzy contractive mappings in a fuzzy metric space |
| topic | fixed points <i>α</i>-<i>η</i>-Γ<i>F</i>-fuzzy contractive map <i>α</i>-Γ<i>F</i>-fuzzy contractive map <i>α</i>-admissible nonlinear fractional differential equation fuzzy metric space |
| url | https://www.mdpi.com/2227-7390/10/16/2831 |
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