Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability
This study presents two novel frameworks, termed a quasi-modular <i>b</i>-metric space and a non-Archimedean quasi-modular <i>b</i>-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/10/558 |
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| author | Ekber Girgin Abdurrahman Büyükkaya Neslihan Kaplan Kuru Mudasir Younis Mahpeyker Öztürk |
| author_facet | Ekber Girgin Abdurrahman Büyükkaya Neslihan Kaplan Kuru Mudasir Younis Mahpeyker Öztürk |
| author_sort | Ekber Girgin |
| collection | DOAJ |
| description | This study presents two novel frameworks, termed a quasi-modular <i>b</i>-metric space and a non-Archimedean quasi-modular <i>b</i>-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several fixed point theorems in the non-Archimedean quasi-modular <i>b</i>-metric space. As a useful application, it also establishes Ulam–Hyers stability for the fixed point problem. Finally, this study concludes with a unique solution to a non-linear fractional differential equation, making a substantial contribution to the discipline. |
| format | Article |
| id | doaj-art-c5ceccd2fe54496ea06acaa0fa38e47e |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-c5ceccd2fe54496ea06acaa0fa38e47e2025-08-20T02:11:04ZengMDPI AGFractal and Fractional2504-31102024-09-0181055810.3390/fractalfract8100558Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers StabilityEkber Girgin0Abdurrahman Büyükkaya1Neslihan Kaplan Kuru2Mudasir Younis3Mahpeyker Öztürk4Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, 54187 Serdivan, Sakarya, TürkiyeDepartment of Mathematics, Karadeniz Technical University, 61080 Ortahisar, Trabzon, TürkiyeDepartment of Mathematics, Sakarya University, 54187 Serdivan, Sakarya, TürkiyeDepartment of Mathematics, Sakarya University, 54187 Serdivan, Sakarya, TürkiyeDepartment of Mathematics, Sakarya University, 54187 Serdivan, Sakarya, TürkiyeThis study presents two novel frameworks, termed a quasi-modular <i>b</i>-metric space and a non-Archimedean quasi-modular <i>b</i>-metric space, and various topological properties are provided. Using comparison and simulation functions, this paper rigorously proves several fixed point theorems in the non-Archimedean quasi-modular <i>b</i>-metric space. As a useful application, it also establishes Ulam–Hyers stability for the fixed point problem. Finally, this study concludes with a unique solution to a non-linear fractional differential equation, making a substantial contribution to the discipline.https://www.mdpi.com/2504-3110/8/10/558fixed pointquasi-modular b-metric spaceUlam–Hyers stabilityfractional differential equation |
| spellingShingle | Ekber Girgin Abdurrahman Büyükkaya Neslihan Kaplan Kuru Mudasir Younis Mahpeyker Öztürk Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability Fractal and Fractional fixed point quasi-modular b-metric space Ulam–Hyers stability fractional differential equation |
| title | Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability |
| title_full | Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability |
| title_fullStr | Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability |
| title_full_unstemmed | Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability |
| title_short | Analysis of Caputo-Type Non-Linear Fractional Differential Equations and Their Ulam–Hyers Stability |
| title_sort | analysis of caputo type non linear fractional differential equations and their ulam hyers stability |
| topic | fixed point quasi-modular b-metric space Ulam–Hyers stability fractional differential equation |
| url | https://www.mdpi.com/2504-3110/8/10/558 |
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