On a combination of fractional differential and integral operators associated with a class of normalized functions

Abstract

Recently, the combined fractional operator (CFO) is introduced and discussed in Baleanu et al. [1] in real domain. In this paper, we extend CFO to the complex domain and study its geometric properties in some normalized analytic functions including the starlike and convex functions. Moreover, we employ the complex CFO to modify a class of Briot-Bouquet differential equations in a complex region. As a consequence, the upper solution is illustrated by using the concept of subordination inequality.