In this paper we have introduced two new classes $\mathcal{HR}_p(\beta,\lambda,k,v)$, $\overline{\mathcal{HR}_p}(\beta,\lambda,k,v)$ of complex valued harmonic multivalent functions of the form $f=h+\overline g$, where $h$ and $g$ are analytic in the unit disk $\Delta=\{z:|z|<1\}$ and $f(z)$ satisfying the condition \[ Re(1-\lambda)\frac{D^vf}{z^p}+\lambda(1-k)\frac{(D^vf)'}{(z^p)'}+\lambda k\frac{(D^vf)''}{(z^p)''}>\frac{\beta}{p}. \] A sufficient coefficient condition for this function in the class$\mathcal{HR}_p(\beta,\lambda,k,v)$ and a necessary and sufficient coefficient condition for the function f in the class $\overline{\mathcal{HR}_p}(\beta,\lambda,k,v)$ are determined. We investigate inclusion relations, distortion theorem, extreme points, convex combination and other interesting properties for these families.