Existence of Solutions and Ulam Stability Analysis of Implicit (p, q)-Fractional Difference Equations
Contemporary Mathematics (Singapore), cilt.6, sa.6, ss.7619-7635, 2025 (ESCI, Scopus)
- 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.