New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces
This study explores innovative insights into the realms of dynamic programming and fractional differential equations, situated explicitly within the framework of partial modular <i>b</i>-metric spaces enriched with a binary relation <inline-formula><math xmlns="http://www.w...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/12/724 |
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| Summary: | This study explores innovative insights into the realms of dynamic programming and fractional differential equations, situated explicitly within the framework of partial modular <i>b</i>-metric spaces enriched with a binary relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>, proposing a novel definition for a generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℷ</mo><mi>C</mi></msub></semantics></math></inline-formula>-type Suzuki <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-contraction specific to these spaces. By doing so, we pave the way for a range of relation-theoretical common fixed-point theorems, highlighting the versatility of our approach. To illustrate the practical relevance of our findings, we present a compelling example. Ultimately, this work aims to enrich the existing academic discourse and stimulate further research and practical applications within the field. |
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| ISSN: | 2504-3110 |