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Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo \emph{et al}. \cite{SaigoMaeda1996} evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable $H$-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable $H$-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, Erd\'{e}lyi-Kober and Saigo operators, associated with multivariable $H$-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.
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참고문헌 (20)
참고문헌 신청
A. A. Kilbas / 2005 / Fractional calculus of the generalized Wright function / Fract. Calc. Appl. Anal 8(2):113~126
A. A. Kilbas / 1998 / Fractional calculus of the H-function / Fukuoka Univ. Sci. Rep 28(2):41~51
A. A. Kilbas / 2008 / Generalized fractional differentiation of Bessel function of the first kind / Math. Balkanica (N. S.) 22(3-4):323~346
D. Kumar / 2013 / Generalized fractional differentiation of the H-function in-volving general class of polynomials / Int. J. Pure Appl. Sci. Technol 16(2):42~53
A. M. Mathai / 1978 / The H-Function with Application in Statistics and Other Disciplines / John Wiley & Sons. Inc
A. A. Kilbas / 1998 / Fractional calculus of the H-function / Fukuoka Univ. Sci. Rep 28(2):41~51
A. A. Kilbas / 2008 / Generalized fractional differentiation of Bessel function of the first kind / Math. Balkanica (N. S.) 22(3-4):323~346
D. Kumar / 2013 / Generalized fractional differentiation of the H-function in-volving general class of polynomials / Int. J. Pure Appl. Sci. Technol 16(2):42~53
A. M. Mathai / 1978 / The H-Function with Application in Statistics and Other Disciplines / John Wiley & Sons. Inc
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