Integral transforms defined by a new fractional class of analytic function in a complex Banach space

TL;DR

This paper introduces a new class of fractional analytic functions in complex Banach spaces, defining associated differential and integral operators, and investigates their boundedness and compactness properties.

Contribution

It presents a novel fractional class of analytic functions with functional parameters and defines related differential and integral operators in Banach spaces.

Findings

Defined a new fractional class of analytic functions with functional parameters

Introduced fractional differential and integral operators in the sense of Ruscheweyh and Noor

Analyzed boundedness and compactness of these operators in complex Banach spaces

Abstract

In this work, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.