On the Ulam-type stability of higher-order iterative Volterra integro-delay differential equations

Pinelas S., Tunç C., Tunç O., Oğuz M. Ş.

AIMS Mathematics, cilt.11, sa.1, ss.1219-1238, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/math.2026052
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1219-1238
  • Anahtar Kelimeler: Banach fixed point theorem, Bielecki metric, higher order, integro-delay differential equation, iterative methods, Ulam-type stability
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this study, we addressed a higher-order iterative Volterra integro-delay differential equation (HOIVIDDE) involving two variable time delays. Our primary focus was on establishing the uniqueness of solutions and analyzing Ulam-type stability properties of the considered HOIVIDDE. We presented three novel results concerning Ulam–Hyers–Rassias (U-H-R), σ-semi-Ulam–Hyers (σsemi-U-H), and Ulam–Hyers (U-H) stability for HOIVIDDE, along with uniqueness results for the associated initial value problem (IVP). The analysis was conducted using the properties of iterative functions, the Banach fixed point theorem, and the Bielecki metric. Notably, this was the first study that extended and enhanced these qualitative properties to an nth-order HOIVIDDE. To illustrate the applicability of the results obtained here, we provided an example verifying the requirements of the new theorems.