By making use of the fractional differential operator due to Owa and Srivastava, a class of analytic functions ℛ_λ(α, ρ) (0 ≤ ρ ≤ 1, 0 ≤ λ < 1, |α| < π/2) is introduced. The sharp bound for the nonlinear functional is found. Several basic properties such as inclusion, subordination, integral transform, Hadamard product are also studied.

By making use of an integral operator due to Noor, a new subclass of analytic functions, denoted by k–$\mathscr{UCV}_n$ (n $\in$ N0 := {0,1,2,...};0 ≤ k < ∞); is introduced. For this class the Fekete-Szegö problem is completely settled. The results obtained here also give the Fekete-Szegö inequalities for the classes of k-uniformly convex functions and k-parabolic starlike functions.