More generalization of fractional calculus. (English) Zbl 0926.26003

Saigo, Megumi; Maeda, Nobuyuki

Rusev, P. (ed.) et al., Transform methods and special functions. Proceedings of the 2nd international workshop, Varna, Bulgaria, August 23–30, 1996. Sofia: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics. 386-400 (1998).

In this paper a generalization of operators of fractional integration introduced by the first author in the eighteeth containing the Appell function \(F_3\) in the kernel is investigated. Mapping properties in McBride spaces \(F_{p,\mu}\) and index laws are proved.
For the entire collection see [Zbl 0914.00065].

Reviewer: H.-J.Glaeske (Jena)

MSC:

26A33	Fractional derivatives and integrals
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

fractional integrals and derivatives; Appell function \(F_3\); McBride spaces; index laws