Communications of the Korean Mathematical Society (대한수학회논문집)

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FRACTIONAL CALCULUS OPERATORS OF THE PRODUCT OF GENERALIZED MODIFIED BESSEL FUNCTION OF THE SECOND TYPE

  • Received : 2020.07.20
  • Accepted : 2020.12.16
  • Published : 2021.07.31
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Abstract

In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric 2F1(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.

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Acknowledgement

The authors express their deepest thanks to the worthy Editor(s) and referee for his/her valuable comments and suggestions that helped to improve this paper in its present form. This work is supported by the Competitive Research Scheme (CRS) project funded by the TEQIP-III (ATU) Rajasthan Technical University Kota under grant number TEQIP-III/RTU(ATU)CRS/2019-20/50.

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