Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with caputo derivatives

Graef J. R., Tunç C., Şevli H.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.103, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 103
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.cnsns.2021.106037
  • Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Volterra integro-fractional delay differential equations, Caputo fractional derivatives, Uniformly stability, Asymptotically stability, Mittag-Leffler stability, Boundedness of solutions, Razumikhin method, STABILITY, SYSTEM
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. The technique of proof involves the Razumikhin method with an appropriate Lyapunov function. For illustrative purposes, two examples are provided. (C) 2021 Published by Elsevier B.V.