In the present work, we begin our investigation with some dynamic properties of new generalized difference operator $\Delta_h^{\alpha,\beta,\gamma}$, defined in Baliarsingh \cite{P2016}. Combining this operator with the well known Ces{à}ro operator, we also introduce new classes of generalized Ces{à}ro summable difference sequence spaces $w(\Delta_h^{\alpha,\beta,\gamma},p),w_0(\Delta_h^{\alpha,\beta,\gamma},p) $ and $w_\infty(\Delta_h^{\alpha,\beta,\gamma},p)$, which are the natural extension of the spaces $w^p, ~w_0^p$ and $w_\infty^p$ defined in \cite{fbasar} and $w_0(p),~w(p), ~\text{and}~w_\infty(p)$ defined by Maddox \cite{maddox}. We establish various topological properties on these spaces along with some inclusion relations with other basic sequence spaces. Further, our investigation is carried out to determine $\alpha^*$- and $\beta^*$- duals and characterize matrix transformations on these spaces.