The Principle of Differential Subordination and Its Application to Analytic and <i>p</i>-Valent Functions Defined by a Generalized Fractional Differintegral Operator

Abstract

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

Keywords

• analytic function
• Hadamard product
• differential subordination
• differential superordination
• generalized fractional differintegral operator