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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.
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참고문헌 (8)
참고문헌 신청
J. D. Griffiths / 2005 / Generalization of the modified Bessel function and its generating function / Fract. Calc. Appl. Anal 8(3):267~276
O. Khan / 2020 / Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3 / AIMS Math 5(2):1462~1475
A. A. Kilbas / 2008 / Generalized fractional differentiation of Bessel function of the first kind / Math. Balkanica 22(3-4,):323~346
A. A. Kilbas / 2008 / Generalized fractional integration of Bessel function of the first kind / Integral Transforms Spec. Funct 19(11-12):869~883
A. A. Kilbas / 2010 / Fractional integration of the product of Bessel functions of the first kind / Fract. Calc. Appl. Anal 13(2):159~175
O. Khan / 2020 / Fractional calculus of a product of multivariable Srivastava polynomial and multi-index Bessel function in the kernel F3 / AIMS Math 5(2):1462~1475
A. A. Kilbas / 2008 / Generalized fractional differentiation of Bessel function of the first kind / Math. Balkanica 22(3-4,):323~346
A. A. Kilbas / 2008 / Generalized fractional integration of Bessel function of the first kind / Integral Transforms Spec. Funct 19(11-12):869~883
A. A. Kilbas / 2010 / Fractional integration of the product of Bessel functions of the first kind / Fract. Calc. Appl. Anal 13(2):159~175
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