Fractional operators and some special functions

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• 作者：Margarita Rivero ; Luis Rodrí ; guez-Germá ; Juan J. Trujillo ; M. Pilar Velasco
• 关键词：Fractional calculus ; Riemann– ; Liouville operators ; Special functions ; Integral representation
• 刊名：Computers and Mathematics with Applications
• 出版年：2010
• 出版时间：March 2010
• 年：2010
• 卷：59
• 期：5
• 页码：1822-1834
• 全文大小：614 K

文摘

This paper considers the Riemann–Liouville fractional operator as a tool to reduce linear ordinary equations with variable coefficients to simpler problems, avoiding the singularities of the original equation. The main result is that this technique allow us to obtain an extension of the classical integral representation of the special functions related with the original differential equations. In particular, we will use as examples the cases of the well-known Generalized, Gauss and Confluent Hypergeometric equations, Laguerre equation, Hermite equation, Legendre equation and Airy equation.