New results on an impulsive differential equation involving a q-analogue of the ψ-Caputo fractional derivative

Ali M. A. A., Thabet S. T. M., Abdeljawad T., Kedim I.

Boundary Value Problems, cilt.2025, sa.1, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1186/s13661-025-02133-4
  • Dergi Adı: Boundary Value Problems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Existence and uniqueness, Fixed point theorems, q-calculus, ψ-Caputo fractional derivative, ψ-Caputo fractional impulsive q-differential equation
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

This paper presents new developments in quantum fractional calculus by introducing the q-analogues of the left and right (L&R) sided ψ-Caputo fractional derivatives (CFDs), and also establishes some essential properties of these novel operators. As an implementation of these new operators, we investigate the existence and uniqueness (EaU) of solutions for a new class of impulsive differential equations involving the q-analogue of the left-side ψ-CFD, by employing Banach’s and Krasnoselskii’s fixed point theorems (FPTs), and supporting with illustrative examples. The introduced operators are more general than the existing operators, such as q-CFD and the classical CFD.