Sylvester-Type Delay Differential Systems Driven by Tempered Fractional Operators With Arbitrary Kernel
Mathematical Methods in the Applied Sciences, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1002/mma.71005
- Dergi Adı: Mathematical Methods in the Applied Sciences
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: delay differential equation, existence and uniqueness, Sylvester-type matrix system, tempered ω-fractional derivative, Ulam–Hyers stability
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
This paper investigates a class of tempered fractional Sylvester-type delay matrix systems defined with arbitrary kernel. A tempered delay perturbation matrix function is introduced and employed to derive explicit solution representations for the corresponding linear problem. The obtained formulation provides a systematic framework for the analysis of matrix-valued delay systems involving generalized tempered memory effects. Furthermore, the stability in the sense of Ulam-Hyers of the linear system is established. The analysis is then extended to a semi-linear setting. By applying the Banach fixed-point theorem, sufficient conditions ensuring the existence and uniqueness of solutions are obtained. In addition, Ulam-Hyers stability results for the semi-linear system are derived. Finally, numerical examples are presented to illustrate the applicability of the theoretical findings.