Fractional calculus operators of the product of generalized modified Bessel function of the second type
Commun. Korean Math. Soc.
Published online February 25, 2021
Ritu Agarwal, Naveen Kumar, Rakesh Kumar Parmar, and Sunil Dutt Purohit
Malaviya National Institute of Technology, Jaipur, University College of Engineering and Technology, Bikaner, Rajasthan Technical University, Kota
Abstract : In this present paper, we consider four integral and differential 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 generalized modified Bessel function of the second type are established. The results are obtained in terms of 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 : 33C05, 33C10, 33C65
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