Growth properties of solutions of linear difference equations with coefficients having $\varphi$-order

"In this paper, we investigate the relations between growth of entire coefficients and that solutions complex homogeneous non-homogeneous linear difference equations with $% \varphi $-order by using a slow scale, $\varphi $-order, where $ is non-decreasing unbounded function. We extend some precedent results due to Zheng Tu (2011) [15] others."