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arXiv · 1703.01912

Fractional calculus and generalized Mittag-Leffler type functions

Christian Lavault
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Abstract

In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and K-function. In the next Section 2 we first recall some generalized fractional integral operators among the most widely used in fractional calculus. Section 3 is devoted to the definitions of M-series and K-function and their relations to special functions. In Sections 4 and 5, effective fractional calculus of the generalized M-series and the K-function is carried out. The last section briefly concludes and opens up new perspectives. The results established herein generalize recent properties of generalized Mittag-Leffler type functions using left-and right-sided generalized fractional differintegral operators. The note results also in important applications in physics and mathematical engineering.

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Christian Lavault. 2017-03-03. Fractional calculus and generalized Mittag-Leffler type functions. https://arxiv.org/abs/1703.01912

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