In this paper we use the principle of subordination between analytic functions and the convolution to introduce the class $\tilde S(f,g;A,B;\alpha,\beta)$. We obtain coefficient inequalities, distortion theorems, extreme points, radii of close to convexity, starlikeness and convexity for this class and modified Hadamard product of several functions belonging to it. Also, we investigate several distortion inequalities involving fractional calculus. Finally, we obtain integral means for functions belonging to this class.