Hyers–Ulam–Rassias stability of fractional delay differential equations with Caputo derivative

Benzarouala C., Tunç C.

Mathematical Methods in the Applied Sciences, vol.47, no.18, pp.13499-13509, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 18
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.10202
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.13499-13509
  • Keywords: Caputo derivative, fractional differential equation, HUR stability, multiple variable delays, the alternative fixed point theorem
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper is devoted to the study of Hyers–Ulam–Rassias (HUR) stability of a nonlinear Caputo fractional delay differential equation (CFrDDE) with multiple variable time delays. We obtain two new theorems with regard to HUR stability of the CFrDDE on bounded and unbounded intervals. The method of the proofs is based on the fixed point approach. The HUR stability results of this paper have indispensable contributions to theory of Ulam stabilities of CFrDDEs and some earlier results in the literature.