Generalized Fractional Integral Operator in a Complex Domain

A new fractional integral operator is used to present a generalized class of analytic functions in a complex domain. The method of definition is based on a Hadamard product of analytic function, which is called convolution product. Then we formulate a convolution integral operator acting on the sub-class of normalized analytic functions. Consequently, we investigate the suggested convolution operator geometrically. Differential subordination inequalities, taking the starlike formula are given. Some consequences of well-known results are illustrated. Keywords: Analytic function, subordination and superordination, univalent function, open unit disk, fractional integral operator, convolution operator, fractional calculus.