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Studies on Generalized Fractional Operators in Complex Domain

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Mathematics Without Boundaries

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Abstract

In the geometric function theory much attention is paid to various fractional operators (differential and integrals) mapping the class of univalent functions and its subclasses into themselves. Recently these operators have applications in different fields such as mathematical physics and computer sciences. In this note we shall introduce a generalized fractional differential operator for the class of univalent functions by employing the Srivastava-Owa fractional differential operator in the unit disk. Geometric properties such as convexity are discussed. Topological properties such as boundedness and compactness are studied in different spaces. Furthermore, conditions are given for the generalized fractional integral operator to be bounded in Hardy space.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Rabha W. Ibrahim

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  1. Rabha W. Ibrahim
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Correspondence to Rabha W. Ibrahim .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Ibrahim, R. (2014). Studies on Generalized Fractional Operators in Complex Domain. In: Rassias, T., Pardalos, P. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1106-6_11

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