IJAM: Volume 37, No. 4 (2024)

DOI: 10.12732/ijam.v37i4.1

GENERALIZED ERDELYI-KOBER

FRACTIONAL INTEGRALS

WITH I-FUNCTION AS KERNEL

V. Kiryakova 1, J. Paneva-Konovska 2,§

1,2 Institute of Mathematics and Informatics

Bulgarian Academy of Sciences

’Acad. G. Bontchev’ Str., Block 8

Sofia – 1113, BULGARIA

Abstract. The Erdelyi-Kober fractional integrals and derivatives are variants of the Riemann-Liuoville with very wide applications due to the freedom to chose their three arbitrary parameters. In this paper we introduce and study a generalization of the Erdelyi-Kober operators of fractional integration where the elementary kernel-function is replaced by a suitably chosen

I^{1,0}_{1,1}-function. The I-functions are generalized hypergeometric functions, introduced by Rathie in 1997 as extensions of the Fox H-functions and Meijer G-functions, but have been not popular because of their rather complicated structure and multivalued behaviour. However, it happens that they are useful not only in statistical physics, but include also important special functions in mathematics. In our previous works we related the I-functions to some specific special functions of fractional calculus, among which analogues of the Mittag-Leffler and

Le Roy type functions. Here, we propose a theory of an I-function generalization of the Erdelyi-Kober fractional integrals, that will serve further as a base for further extension of the generalized fractional calculus with operators of fractional multi-order.

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How to cite this paper?
DOI: 10.12732/ijam.v37i4.1
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 4

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