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arXiv · 1304.1058

On Some Operators Involving Hadamard Derivatives

Roberto Garra·Federico Polito
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Abstract

In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the utility of these results to solve some integro-differential equations involving these operators by means of operational methods. We show the advantage of our approach through some examples. Among these, an application to a modified Lamb--Bateman integral equation is presented.

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Roberto Garra, Federico Polito. 2013-03-26. On Some Operators Involving Hadamard Derivatives. https://doi.org/10.1080/10652469.2012.756875

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