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

Abstract

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.