Subordination and inclusion theorems for higher order derivatives of a generalized fractional differintegral operator

Abstract

Abstract The main object of this paper is to investigate some subordination results of certain subclasses of multivalent analytic functions which are defined by a generalized fractional differintegral operator. Inclusion relations for functions in the class Sp,qλ,μ,ηζ;A,B $\mathcal {S}_{p,q}^{\lambda,\mu,\eta }\left (\zeta ;A,B\right) \ $ and the images of these functions by the generalized Bernardi-Libera-Livingston integral operator are also considered.

Keywords

• Differential subordination
• Multivalent functions
• Higher order derivatives
• Generalized fractional differintegral operator