In this paper, we introduce the subclass $S_{j}(n,p,q,\alpha)$ of analytic and $p$-valent functions with negative coefficients defined by new operator $D_{p}^{n}$. In this paper we give some properties of functions in the class $S_{j}(n,p,q,\alpha)$ and obtain numerous sharp results including (for example) coefficient estimates, distortion theorem, radii of close-to-convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class $S_{j}(n,p,q,\alpha)$. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.