Impulsive implicit fractional q-integrodifferential equations under Riemann–Liouville boundary conditions with stability results

Abstract

We aim to analyze a novel class of impulsive implicit $q$-integrodifferential equations of fractional order involving a certain kind of boundary value problem with mixed Riemann–Liouville fractional $q$-integral boundary conditions. Base on the theorems of nonlinear analysis, we investigate the existence and uniqueness results for the given $q$-fractional equations. In addition to, the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias are examined. Finally, some illustrative examples guarantee our outcomes.