Existence of Solutions and Ulam Stability Analysis of Implicit (p, q)-Fractional Difference Equations

Mesmouli M. B., Iambor L. F., Tunç O., Hassan T. S.

Contemporary Mathematics (Singapore), cilt.6, sa.6, ss.7619-7635, 2025 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.37256/cm.6620258140
  • Dergi Adı: Contemporary Mathematics (Singapore)
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.7619-7635
  • Anahtar Kelimeler: (p,q)-fractional difference calculus, (p,q)-Gronwall inequality, fixed point theorem, generalized Ulam-Hyers-Rassias stability, implicit equation
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper studies the existence theorems and Ulam stability results of solutions for implicit (p, q)-fractional difference equations. By applying Banach and Schauder fixed-point principles, we derive results related to the existence and uniqueness of solutions. Additionally, we analyze generalized Ulam-Hyers stability under (p, q)-Gronwall inequality. Key results are supported with illustrative examples, demonstrating the applicability of the proposed framework. Compared to previous studies restricted to the standard q-calculus, the present work introduces the (p, q)-Caputo fractional difference setting, which offers a more flexible and generalized approach. This novelty extends existing results and provides new perspectives for the analysis of stability and solvability of fractional systems.