Boundedness of normalization generalized differential operator of fractional formal

TL;DR

This paper introduces a new generalized fractional differential operator extending Srivastava-Owa operators, and studies its geometric properties, boundedness, and compactness in function spaces using hypergeometric functions.

Contribution

It defines a novel generalized fractional differential operator and analyzes its geometric and boundedness properties, expanding the understanding of fractional calculus operators.

Findings

Operator exhibits univalency, starlikeness, and convexity under certain conditions.

Boundedness and compactness are established in Bloch space.

Uses hypergeometric functions to analyze operator properties.

Abstract

Many authors have considered and investigated generalized fractional differential operators. The main object of this present paper is to define a new generalized fractional differential operator $\mathfrak{T}^{\beta,\tau,\gamma},$ which generalized the Srivastava-Owa operators. Moreover, we investigate of the geometric properties such as univalency, starlikeness, convexity for their normalization. Further, boundedness and compactness in some well known spaces, such as Bloch space for last mention operator also are considered. Our tool is based on the generalized hypergeometric function.