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

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      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.

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      On development of fractional calculus during the last fifty years

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        Uniformly Convex Functions and a Corresponding Class of Starlike Functions

         Frode Ronning (1993)
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          Classes of analytic functions with fractional powers defined by means of a certain linear operator

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            Author and article information

            Journal
            1601.03142

            Functional analysis

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