Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions

In the present paper, we study a new class of boundary value problems for Langevin quantum difference equations with multi-quantum numbers q-derivative nonlocal conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is established by Banach s contraction mapping principle, while the existence of solutions is derived by using Krasnoselskii s fixed point theorem and Leray-Schauder s nonlinear alternative. Examples illustrating the results are also presented.