On the Existence of Solutions and Ulam-Type Stability for a Nonlinear ψ-Hilfer Fractional-Order Delay Integro-Differential Equation

Tunç C., Alshammari F. S., Akyıldız F. T.

Fractal and Fractional, cilt.9, sa.7, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 7
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/fractalfract9070409
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: fixed-point approach, semi-UHR stability, UH stability, UHR stability, unique solution, ψ-Hilfer FrOVI-DE
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this work, we address a nonlinear (Formula presented.) -Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the (Formula presented.) -Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam–Hyers–Rassias stability, semi-Ulam–Hyers–Rassias stability, and Ulam–Hyers stability of the proposed (Formula presented.) -Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on (Formula presented.) -Hilfer fractional-order Volterra integro-differential equations, both including and excluding single delay, by establishing new findings for nonlinear (Formula presented.) -Hilfer fractional-order Volterra integro-differential equations involving n-multiple-variable time delays. This study provides novel theoretical insights that deepen the qualitative understanding of fractional calculus.