# Some Fractional Calculus results associated with the $I$-Function

Source: [Some Fractional Calculus results associated with the $I$-Function](<https://www.sota2.com/research/paper/68fa53d51e209131ce986864>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:40:20.181Z

Authors: K. K. Kataria, P. Vellaisamy

Published: 2014-08-25T13:18:59.000Z

## Abstract

The effect of Marichev-Saigo-Maeda (MSM) fractional operators involving third Appell function on the $I$ function is studied. It is shown that the order of the $I$-function increases on application of these operators to the power multiple of the $I$-function. The Caputo-type MSM fractional derivatives are introduced and studied for the $I$-function. As special cases, the corresponding assertions for Saigo and Erd\\'elyi-Kober fractional operators are also presented. The results obtained in this paper generalize several known results obtained recently in the literature.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1408.5745>)

[PDF](<https://arxiv.org/pdf/1408.5745.pdf>)