Ulam-Hyers stability for impulsive fractional differential equations in nonreflexive Banach spaces

Jabeen T., Khalid F., Jhangeer A., Muddassar M., BUDAK H., Musharaf H. M.

Boundary Value Problems, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1186/s13661-026-02275-z
  • Dergi Adı: Boundary Value Problems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Banach space methods, Caputo-type fractional operators, Fixed point methods, Impulsive system, Nonlinear boundary conditions, Satbility analysis
  • Kocaeli Üniversitesi Adresli: Evet

Özet

This paper investigates the existence, uniqueness, and Ulam–Hyers stability of solutions for a class of impulsive multi-term fractional differential equations in nonreflexive Banach spaces. The considered system is formulated in the sense of Caputo fractional derivatives with respect to an increasing function and incorporates nonlinear boundary conditions together with impulsive effects. By transforming the given problem into an equivalent integral equation, sufficient conditions ensuring the existence and uniqueness of solutions are derived via Banach’s fixed point theorem. Furthermore, the Ulam–Hyers stability of the proposed model is established, guaranteeing that approximate solutions remain uniformly close to the exact solution under suitable conditions. The obtained results generalize and extend several existing contributions in the literature on fractional differential equations by including impulsive dynamics and the setting of nonreflexive Banach spaces. Finally, illustrative examples are presented to confirm the applicability and effectiveness of the theoretical results.