Existence and Uniqueness of Solution for Quantum Fractional Pantograph Equations

In this paper, the fractional pantograph equations in quantum calculus are studied. We propose a q-fractional variant of the nonlinear pantograph equation with a given initial condition and a nonlinear neutral q-fractional pantograph equation. Based on the fixed-point theory, the main theorems provide some new results regarding the existence and uniqueness of solutions for q-fractional pantograph equations.