Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability

Mahmudov N.

Journal of Applied Mathematics, vol.2022, 2022 (ESCI, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 2022
  • Nəşr tarixi: 2022
  • Doi nömrəsi: 10.1155/2022/2661343
  • jurnalın adı: Journal of Applied Mathematics
  • Jurnalın baxıldığı indekslər: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system D0,tμ,νzt+Azt+Ωzt-h=ft of order 1<μ<2 and type 0≤ν≤1, with nonpermutable matrices A and Ω. Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear time-delay systems with permutable matrices and new even for these fractional delay systems.