Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches
In this work, we investigate the theoretical properties of a generalized coupled system of finite-delay fractional differential equations involving Caputo derivatives. We establish rigorous criteria to ensure the existence and uniqueness of solutions under appropriate assumptions on the problem para...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/7/1113 |
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| author | Meraa Arab Mohammed S. Abdo Najla Alghamdi Muath Awadalla |
| author_facet | Meraa Arab Mohammed S. Abdo Najla Alghamdi Muath Awadalla |
| author_sort | Meraa Arab |
| collection | DOAJ |
| description | In this work, we investigate the theoretical properties of a generalized coupled system of finite-delay fractional differential equations involving Caputo derivatives. We establish rigorous criteria to ensure the existence and uniqueness of solutions under appropriate assumptions on the problem parameters and constituent functions, employing contraction mapping principles and Schauder’s fixed-point theorem. Then, we examine the Ulam–Hyers stability of the proposed system. To illustrate the main findings, three examples are provided. Moreover, we provide numerical solutions using the Adams–Bashforth–Moulton method. The practical significance of our results is demonstrated through illustrative examples, highlighting applications in predator–prey dynamics and control systems. |
| format | Article |
| id | doaj-art-228072e35e044249b5d75fb25160c982 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-228072e35e044249b5d75fb25160c9822025-08-20T03:06:20ZengMDPI AGMathematics2227-73902025-03-01137111310.3390/math13071113Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical ApproachesMeraa Arab0Mohammed S. Abdo1Najla Alghamdi2Muath Awadalla3Department of Mathematics and Statistics, College of Science, King Faisal University, Ahsa 31982, Saudi ArabiaDepartment of Mathematics, Hodeidah University, Al Hudaydah 3114, YemenDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Ahsa 31982, Saudi ArabiaIn this work, we investigate the theoretical properties of a generalized coupled system of finite-delay fractional differential equations involving Caputo derivatives. We establish rigorous criteria to ensure the existence and uniqueness of solutions under appropriate assumptions on the problem parameters and constituent functions, employing contraction mapping principles and Schauder’s fixed-point theorem. Then, we examine the Ulam–Hyers stability of the proposed system. To illustrate the main findings, three examples are provided. Moreover, we provide numerical solutions using the Adams–Bashforth–Moulton method. The practical significance of our results is demonstrated through illustrative examples, highlighting applications in predator–prey dynamics and control systems.https://www.mdpi.com/2227-7390/13/7/1113Caputo fractional derivativeexistence and stabilityfixed-point theoremsAdams–Bashforth–Moulton method |
| spellingShingle | Meraa Arab Mohammed S. Abdo Najla Alghamdi Muath Awadalla Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches Mathematics Caputo fractional derivative existence and stability fixed-point theorems Adams–Bashforth–Moulton method |
| title | Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches |
| title_full | Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches |
| title_fullStr | Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches |
| title_full_unstemmed | Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches |
| title_short | Analyzing Coupled Delayed Fractional Systems: Theoretical Insights and Numerical Approaches |
| title_sort | analyzing coupled delayed fractional systems theoretical insights and numerical approaches |
| topic | Caputo fractional derivative existence and stability fixed-point theorems Adams–Bashforth–Moulton method |
| url | https://www.mdpi.com/2227-7390/13/7/1113 |
| work_keys_str_mv | AT meraaarab analyzingcoupleddelayedfractionalsystemstheoreticalinsightsandnumericalapproaches AT mohammedsabdo analyzingcoupleddelayedfractionalsystemstheoreticalinsightsandnumericalapproaches AT najlaalghamdi analyzingcoupleddelayedfractionalsystemstheoreticalinsightsandnumericalapproaches AT muathawadalla analyzingcoupleddelayedfractionalsystemstheoreticalinsightsandnumericalapproaches |