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 Fractional calculus operators of the product of generalized modified Bessel function of the second type Commun. Korean Math. Soc. 2021 Vol. 36, No. 3, 557-573 https://doi.org/10.4134/CKMS.c200254Published online February 25, 2021Printed July 31, 2021 Ritu Agarwal, Naveen Kumar, Rakesh Kumar Parmar, Sunil Dutt Purohit Malaviya National Institute of Technology; Malaviya National Institute of Technology; University College of Engineering and Technology; Rajasthan Technical University Abstract : In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric ${}_2{F}_1(x)$ function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erd\'elyi-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 Erd\'elyi-Kober (E-K) fractional integral and differential are also deduced. Keywords : Saigo fractional calculus operators, generalized Lauricella function, Gauss' hypergeometric ${}_2{F}_1(x)$ function, generalized modified Bessel function of the second type MSC numbers : 26A33, 33C10, 33C20, 33C50, 33C60, 26A09 Supported by : 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. Downloads: Full-text PDF   Full-text HTML

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