Mesmouli, Mouataz BillahIambor, Loredana FlorentinaTunc, OsmanHassan, Taher S.2025-11-302025-11-3020252705-10642705-105610.37256/cm.66202581402-s2.0-105021804177https://doi.org/10.37256/cm.6620258140This 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.eninfo:eu-repo/semantics/openAccessImplicit Equation(P,Q)-Fractional Difference CalculusFixed Point Theorem(P,Q)-Gronwall InequalityGeneralized Ulam-Hyers-Rassias StabilityArticle