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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

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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
                2016-01-13
                Article
                1601.03142
                6d512308-7a6b-48a7-adea-35082a87e772

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                14 pages
                math.FA

                Functional analysis
                Functional analysis

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