New results concerning fuzzy differential subordination theory are obtained in this paper using the operator denoted by Dz−λLαn, previously introduced by applying the Riemann–Liouville fractional integral to the convex combination of well-known Ruscheweyh and Sălăgean differential operators. A new fuzzy subclass DLnFδ,α,λ is defined and studied involving the operator Dz−λLαn. Fuzzy differential subordinations are obtained considering functions from class DLnFδ,α,λ and the fuzzy best dominants are also given. Using particular functions interesting corollaries are obtained and an example shows how the obtained results can be applied.