The aim of the present paper is to show several properties of functions belonging to a subclass $M_{n,\mathrm{\Omega }}^p(A,B,\lambda ,b)$ (where $b$ is complex number with $\mathbf{Re}(b)>0$ and $A$ ve $B$ are two arbitrary constants with $-1\le B<A\le 1$). Coefficient estimates and some distortion theorems for this class of functions are obtained. For this class we also derive the radii of close-to-convexity, starlikeness, and convexity. Further, an application involving fractional calculus for functions in $M_{n,\mathrm{\Omega }}^p(A,B,\lambda ,b)$ is given.