A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations
This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/5/270 |
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| author | Nawal Alharbi Nawab Hussain |
| author_facet | Nawal Alharbi Nawab Hussain |
| author_sort | Nawal Alharbi |
| collection | DOAJ |
| description | This study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best proximity-point theorems for both single-valued and multivalued mappings, thereby broadening the scope of fuzzy analysis. Furthermerefore, we have for aore, we apply one of our key results to derive conditions, ensuring the existence and uniqueness of a solution to Hadamard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ψ</mo></semantics></math></inline-formula>-Caputo tempered fuzzy fractional differential equations, particularly in the context of the SIR dynamics model. These theoretical advancements are expected to open new avenues for research in fuzzy fixed-point theory and its applications to hybrid models within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-fuzzy metric spaces. |
| format | Article |
| id | doaj-art-e4a38eff1b2c47a4b00e5fe24e8cc736 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-e4a38eff1b2c47a4b00e5fe24e8cc7362025-08-20T02:34:00ZengMDPI AGFractal and Fractional2504-31102025-04-019527010.3390/fractalfract9050270A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential EquationsNawal Alharbi0Nawab Hussain1Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThis study investigates fuzzy fixed points and fuzzy best proximity points for fuzzy mappings within the newly introduced framework <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-fuzzy metric spaces that extends various existing fuzzy metric spaces. We establish novel fixed-point and best proximity-point theorems for both single-valued and multivalued mappings, thereby broadening the scope of fuzzy analysis. Furthermerefore, we have for aore, we apply one of our key results to derive conditions, ensuring the existence and uniqueness of a solution to Hadamard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ψ</mo></semantics></math></inline-formula>-Caputo tempered fuzzy fractional differential equations, particularly in the context of the SIR dynamics model. These theoretical advancements are expected to open new avenues for research in fuzzy fixed-point theory and its applications to hybrid models within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>-fuzzy metric spaces.https://www.mdpi.com/2504-3110/9/5/270<i>θ</i>-fuzzy metric spacefuzzy mappingfuzzy fixed pointfuzzy best proximity pointHadamard Ψ-Caputo tempered fractional derivative |
| spellingShingle | Nawal Alharbi Nawab Hussain A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations Fractal and Fractional <i>θ</i>-fuzzy metric space fuzzy mapping fuzzy fixed point fuzzy best proximity point Hadamard Ψ-Caputo tempered fractional derivative |
| title | A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations |
| title_full | A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations |
| title_fullStr | A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations |
| title_full_unstemmed | A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations |
| title_short | A Study of Fuzzy Fixed Points and Their Application to Fuzzy Fractional Differential Equations |
| title_sort | study of fuzzy fixed points and their application to fuzzy fractional differential equations |
| topic | <i>θ</i>-fuzzy metric space fuzzy mapping fuzzy fixed point fuzzy best proximity point Hadamard Ψ-Caputo tempered fractional derivative |
| url | https://www.mdpi.com/2504-3110/9/5/270 |
| work_keys_str_mv | AT nawalalharbi astudyoffuzzyfixedpointsandtheirapplicationtofuzzyfractionaldifferentialequations AT nawabhussain astudyoffuzzyfixedpointsandtheirapplicationtofuzzyfractionaldifferentialequations AT nawalalharbi studyoffuzzyfixedpointsandtheirapplicationtofuzzyfractionaldifferentialequations AT nawabhussain studyoffuzzyfixedpointsandtheirapplicationtofuzzyfractionaldifferentialequations |