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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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/724 |
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| _version_ | 1846104610537734144 |
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| author | Abdurrahman Büyükkaya Dilek Kesik Ülkü Yeşil Mahpeyker Öztürk |
| author_facet | Abdurrahman Büyükkaya Dilek Kesik Ülkü Yeşil Mahpeyker Öztürk |
| author_sort | Abdurrahman Büyükkaya |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f63c0815858d4d778dcb3eaafa3aa069 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-f63c0815858d4d778dcb3eaafa3aa0692024-12-27T14:27:07ZengMDPI AGFractal and Fractional2504-31102024-12-0181272410.3390/fractalfract8120724New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric SpacesAbdurrahman Büyükkaya0Dilek Kesik1Ülkü Yeşil2Mahpeyker Öztürk3Department of Mathematics, Karadeniz Technical University, 61080 Ortahisar, Trabzon, TürkiyeDepartment of Mathematics, Sakarya University, 54050 Serdivan, Sakarya, TürkiyeDepartment of Mathematical Engineering, Faculty of Chemical Metallurgical Engineering, Yildiz Technical University, 34220 Esenler, Istanbul, TürkiyeDepartment of Mathematics, Sakarya University, 54050 Serdivan, Sakarya, TürkiyeThis 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.https://www.mdpi.com/2504-3110/8/12/724fixed pointpartial modular b-metricbinary relationfractional differential equationsdynamic programming |
| spellingShingle | Abdurrahman Büyükkaya Dilek Kesik Ülkü Yeşil Mahpeyker Öztürk New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces Fractal and Fractional fixed point partial modular b-metric binary relation fractional differential equations dynamic programming |
| title | New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces |
| title_full | New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces |
| title_fullStr | New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces |
| title_full_unstemmed | New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces |
| title_short | New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular <i>b</i>-Metric Spaces |
| title_sort | new studies for dynamic programming and fractional differential equations in partial modular i b i metric spaces |
| topic | fixed point partial modular b-metric binary relation fractional differential equations dynamic programming |
| url | https://www.mdpi.com/2504-3110/8/12/724 |
| work_keys_str_mv | AT abdurrahmanbuyukkaya newstudiesfordynamicprogrammingandfractionaldifferentialequationsinpartialmodularibimetricspaces AT dilekkesik newstudiesfordynamicprogrammingandfractionaldifferentialequationsinpartialmodularibimetricspaces AT ulkuyesil newstudiesfordynamicprogrammingandfractionaldifferentialequationsinpartialmodularibimetricspaces AT mahpeykerozturk newstudiesfordynamicprogrammingandfractionaldifferentialequationsinpartialmodularibimetricspaces |