Subordination results for a fractional integral operator

In this paper, we establish several differential subordinations regarding the operator $D_{z}^{-\lambda }SR^{m,n}$ defined using the fractional integral of the differential operator $SR^{m,n}$, obtained as a convolution product of Sălăgean operator $S^{m}$ and Ruscheweyh derivative $R^{n}$. By means of the newly obtained operator, a new subclass of analytic functions denoted by $\mathcal{SR}_{m,n,\lambda }\left( \delta \right) $ is introduced and various properties and characteristics of this class are derived, making use of the concept of differential subordination.