In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

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