Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays
This study investigates a system of generalized Caputo proportional fractional delay integro-differential equations (CFDIDEs) involving multiple kernels and constant time delays. As key qualitative properties, the stability, asymptotic stability, exponential stability, and boundedness of solutions a...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2025.2537476 |
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| _version_ | 1849728959857557504 |
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| author | Cemil Tunç Kasım Mansız Osman Tunç |
| author_facet | Cemil Tunç Kasım Mansız Osman Tunç |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | This study investigates a system of generalized Caputo proportional fractional delay integro-differential equations (CFDIDEs) involving multiple kernels and constant time delays. As key qualitative properties, the stability, asymptotic stability, exponential stability, and boundedness of solutions are analyzed through four newly established results. The results of the study are established using a suitable Lyapunov function, along with a modified Lyapunov–Razumikhin approach for the vector-valued case. The reliability and relevance of the proposed results are illustrated through two example implementations in particular cases of the system under consideration. The outcomes of this study makes new contributions to qualitative theory of CFDIDEs for vector-based cases. |
| format | Article |
| id | doaj-art-02b7b490928b4c258edfa6e8da0212dd |
| institution | DOAJ |
| issn | 2576-5299 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj-art-02b7b490928b4c258edfa6e8da0212dd2025-08-20T03:09:23ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992025-12-0132124726110.1080/25765299.2025.2537476Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delaysCemil Tunç0Kasım Mansız1Osman Tunç2Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, TurkeyDepartment of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, TurkeyDepartment of Computer, Baskale Vocational School, Van Yuzuncu Yil University, Van, TurkeyThis study investigates a system of generalized Caputo proportional fractional delay integro-differential equations (CFDIDEs) involving multiple kernels and constant time delays. As key qualitative properties, the stability, asymptotic stability, exponential stability, and boundedness of solutions are analyzed through four newly established results. The results of the study are established using a suitable Lyapunov function, along with a modified Lyapunov–Razumikhin approach for the vector-valued case. The reliability and relevance of the proposed results are illustrated through two example implementations in particular cases of the system under consideration. The outcomes of this study makes new contributions to qualitative theory of CFDIDEs for vector-based cases.https://www.tandfonline.com/doi/10.1080/25765299.2025.2537476Boundednessdelay integro-differential equationsgeneralized caputo proportional fractional derivativeLyapunov-Razumikhin approachmultiple delaysstability |
| spellingShingle | Cemil Tunç Kasım Mansız Osman Tunç Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays Arab Journal of Basic and Applied Sciences Boundedness delay integro-differential equations generalized caputo proportional fractional derivative Lyapunov-Razumikhin approach multiple delays stability |
| title | Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays |
| title_full | Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays |
| title_fullStr | Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays |
| title_full_unstemmed | Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays |
| title_short | Qualitative analysis for a system of generalized Caputo proportional fractional integro-differential equations with multiple time delays |
| title_sort | qualitative analysis for a system of generalized caputo proportional fractional integro differential equations with multiple time delays |
| topic | Boundedness delay integro-differential equations generalized caputo proportional fractional derivative Lyapunov-Razumikhin approach multiple delays stability |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2025.2537476 |
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