Fuzzy differential subordinations connected with the linear operator

summary:We obtain several fuzzy differential subordinations by using a linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha }f(z)=z+\sum \limits _{k=2}^{\infty }(1+\gamma ( k-1))^{n}m^{\alpha }(m+k)^{-\alpha }a_{k}z^{k}$. Using the linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha },$ we also introduce a class of univalent analytic functions for which we give some properties