Abstract

This is a continuation (Part 2) of our previous paper (Part 1), [28]. We study the multi-index generalizations (with 3m and 4m indices) of the classical Le Roy function and its Mittag-Leffler analogues, initiated recently by Gerhold, Garra and Polito and then studied by several other authors. In Part 1, along with the basic analytical properties, we provided the Laplace transform of the multi-index Le Roy type functions. Here, for these new special functions we consider the Erdelyi-Kober fractional order integral as one of the basic operators of Fractional Calculus (FC). The results are also specified for the particular cases of the Le Roy type functions as well as for the Riemann-Liouville and other specific cases of this operator. Finally, we propose another more general definition for the multi-index Le Roy functions and alternative interpretations, and mention about the possibilities to relate them with special functions more general than Fox H-function.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 5
Year: 2023

DOI: 10.12732/ijam.v36i5.2

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