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Fractional Integral Operators Characterized by Some New Hypergeometric Summation Formulas

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Abstract

The purpose of this paper is to study generalized fractional integral operators whose kernels involve a very special class of generalized hypergeometric functions r+2Fr+1. The importance of these operators stems from the summability of this special class of generalized hypergeometric functions at unit argument which is realized in the present paper by making use of the Karlsson-Minton type summation theorems. We obtain for these operators several results including the generalized fractional integrals of the H-function, certain mapping properties and their Mellin transforms. Applications to inequalities are also pointed out.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

    Min-Jie Luo

  2. M.P. University of Agriculture and Technology, Rajasthan, India

    Ravinder Krishna Raina

Authors
  1. Min-Jie Luo
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  2. Ravinder Krishna Raina
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Correspondence to Min-Jie Luo.

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Luo, MJ., Raina, R.K. Fractional Integral Operators Characterized by Some New Hypergeometric Summation Formulas. FCAA 20, 422–446 (2017). https://doi.org/10.1515/fca-2017-0022

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  • DOI: https://doi.org/10.1515/fca-2017-0022

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