Weak Solutions and Uniqueness Results for Sequential q‐Fractional Pantograph Equations Under Weak Topology

ABSTRACT The purpose of this paper is to investigate the existence and uniqueness of weak solutions for a nonlinear sequential quantum Liouville–Caputo fractional differential equation subject to a nonlocal initial condition, where the initial value is defined through a continuous function rather than a constant. The main novelty of this work lies in the combination of a sequential quantum fractional operator with a functional nonlocal initial condition. By employing Mönch's fixed point theorem together with the De Blasi measure of weak noncompactness, we establish the existence of a weak solution. Moreover, by imposing suitable Lipschitz conditions and applying Banach's contraction principle, we prove the uniqueness of the weak solution.