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A Generalized Fractional Calculus and Integral Transforms

  • Virginia Kiryakova

Abstract

In this paper a generalized fractional calculus and its applications to different topics in analysis, especially to some integral transforms, are discussed. The kernel-function of the generalized operators of integration of fractional multiorder considered here is a suitably chosen case of Meijer’s G-function:
$${\text{G}}_{{\text{pq}}}^{{\text{mn}}} \left[ {\sigma \left| {\begin{array}{*{20}c} {{\text{a}}_{\text{1}} , \ldots ,{\text{a}}_{\text{p}} } \\ {{\text{b}}_{\text{1}} , \ldots ,{\text{b}}_{\text{q}} } \\ \end{array} } \right.} \right] = \frac{1} {{2\pi {\text{i}}}}\int\limits_L {\frac{{\prod\limits_{{\text{k}} = {\text{1}}}^{\text{m}} {\Gamma \left( {{\text{b}}_{\text{k}} - {\text{s}}} \right)} \prod\limits_{{\text{j}} = {\text{1}}}^{\text{n}} {\Gamma \left( {{\text{1}} - {\text{a}}_{\text{j}} + {\text{s}}} \right)} }} {{\prod\limits_{{\text{k}} = {\text{m}} + {\text{1}}}^{\text{q}} {\Gamma \left( {1 - {\text{b}}_{\text{k}} + {\text{s}}} \right)} \prod\limits_{{\text{j}} = {\text{n}} + {\text{1}}}^{\text{p}} {\Gamma \left( {{\text{a}}_{\text{j}} - {\text{s}}} \right)} }}} \sigma ^{\text{s}} {\text{ds}}\quad \left( {\left[ {\text{1}} \right],\left[ 2 \right]} \right).$$
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Keywords

Fractional Derivative Generalize Operator Fractional Integral Integral Transformation Operational Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Virginia Kiryakova
    • 1
  1. 1.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria

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