On Ulam–Hyers Stable Solutions for a Fractional Dual‐Hybrid q‐Integro‐Difference Problem

This study deals with a theoretical analysis on a fractional q ‐difference dual‐hybrid problem along with dual‐hybrid q ‐integro‐difference conditions. The uniqueness of the q ‐solution for the proposed q ‐difference equation are analyzed via the Banach′s contraction principle. The existence of solutions is analyzed by using the Krasnoselskii′s fixed‐point theorem and the Leray–Schauder nonlinear alternative. Furthermore, the Ulam–Hyers and generalized Ulam–Hyers stability of the considered dual‐hybrid problem are examined. Finally, three illustrative examples are included in both numerical and graphical forms to validate the theoretical results.