Abstract

The paper is devoted to study the generalized fractional calculus of arbitrary complex order for the H -function defined by Inayat Hussain [8]. The classical fractional integrals and derivatives of Riemann-Liouville type are treated. The considered generalized fractional integration and differentiation operators contain the Gauss Hypergeometric function as a kernel and generalize classical Riemann- Liouville, Erdelyi-Kober types ones. It is proved that the generalized fractional integrals and derivatives of H -function turn also out H -functions but of greater order. Especially, the obtained results define more precise and general ones than known. Corresponding assertion for Riemann-Liouville and Erdelyi-Kober fractional integral operators are also presented.

How to Cite
CHAURASIA, V.B.L.; SAXENA, Vishal. Generalized Fractional Calculus Of Certain Product Of Special Functions. Global Journal of Science Frontier Research, [S.l.], v. 10, n. 4, sep. 2010. ISSN 2249-4626. Available at: <https://journalofscience.org/index.php/GJSFR/article/view/178>. Date accessed: 20 jan. 2022.