An Application of the Prabhakar Fractional Operator to a Subclass of Analytic Univalent Function

Abstract

Fractional differential operators have recently been linked with numerous other areas of science, technology and engineering studies. For a real variable, the class of fractional differential and integral operators is evaluated. In this study, we look into the Prabhakar fractional differential operator, which is the most applicable fractional differential operator in a complex domain. In terms of observing a group of normalized analytical functions, we express the operator. In the open unit disc, we deal with its geometric performance. Applying the Prabhakar fractional differential operator dcθα,βγ,ω to a subclass of analytic univalent function results in the creation of a new subclass of mathematical functions: W(γ,ω,α,β,θ,m,c,z,p,q). We obtain the characteristic, neighborhood and convolution properties for this class. Some of these properties are extensions of defined results.

Keywords

• analytic function
• fractional calculus operator
• Hadmard product (convolution)
• hypergeometric function
• neighborhood
• Prabhakar operator