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, vol.9, no.7, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 7
  • Publication Date: 2025
  • Doi Number: 10.3390/fractalfract9070409
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Keywords: fixed-point approach, semi-UHR stability, UH stability, UHR stability, unique solution, ψ-Hilfer FrOVI-DE
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.