Existence, uniqueness and continuous dependence results of coupled system of Hilfer fractional stochastic pantograph equations with nonlocal integral conditions

Abstract

This study explores the existence, uniqueness, and continuous dependence of solutions for coupled system of Hilfer fractional stochastic pantograph equations with nonlocal integral conditions. The existence of solutions is demonstrated using topological degree theory for condensing maps. The uniqueness is established via Banach’s contraction principle. To address continuous dependence, the generalized Gronwall inequality is applied. Additionally, a numerical example is provided to illustrate and confirm the theoretical findings.