A class of nonlinear fractional differential equations with quantum–deformed memory is investigated. The deformation is introduced through a normalized \((q,\tau )\) –Gamma function, which yields a family of \((q,\tau )\) –fractional integral operators recovering the classical fractional kernel in the limit \((q,\tau )\rightarrow (1,1)\) . We prove existence and uniqueness of holomorphic solutions and establish Ulam–Hyers–Rassias stability for the associated nonlinear problem by means of a fixed point approach. Quantitative sensitivity estimates with respect to the deformation parameters \((q,\tau )\) and perturbations of the memory kernel are derived. In particular, a sharp comparison result is obtained between solutions generated by the power–law kernel and those generated by the Mittag–Leffler kernel. These results provide a rigorous basis for kernel selection and robustness analysis in quantum–deformed fractional models.
