# The Generalized $K$-Wright Function and Marichev-Saigo-Maeda Fractional Operators

Source: [The Generalized $K$-Wright Function and Marichev-Saigo-Maeda Fractional Operators](<https://www.sota2.com/research/paper/68fa53d51e209131ce986863>)

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: 2014-08-17T15:00:13.000Z

## Abstract

In this paper, the generalized fractional operators involving Appell's function $F\_3$ in the kernel due to Marichev-Saigo-Maeda are applied to the generalized $K$-Wright function. These fractional operators when applied to power multipliers of the generalized $K$-Wright function ${}\_{p}\\Psi^k\_q$ yields a higher ordered generalized $K$-Wright function, namely, ${}\_{p+3}\\Psi^k\_{q+3}$. The Caputo-type modification of Marichev-Saigo-Maeda fractional differentiation is introduced and the corresponding assertions for Saigo and Erd\\'elyi-Kober fractional operators are also presented. The results derived in this paper generalize several recent results in the theory of special functions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1408.4762>)

[PDF](<https://arxiv.org/pdf/1408.4762.pdf>)