The third boundary value problem for parabolic differential-difference equation in one-dimensional case

This work is concerned with the differential-difference equation u_t-(R_{2Q}u_x)_x+R_{1Q}u_x+R_{0Q}u =f(x,t),quad(x,t)in Q_T, with the boundary conditions left.left(-R_{2Q}u_x+alpha uright)right|_{x=0}=0,quad left.left(R_{2Q}u_x+beta uright)right|_{x=d}=0, quad 0