Fractional operators and some special functions

Authors:
Margarita Rivero;Luis Rodríguez-Germá;Juan J. Trujillo;M. Pilar Velasco
Affiliations:
Universidad de La Laguna, Departamento de Matemática Fundamental, 38271 La Laguna, Tenerife, Spain;Universidad de La Laguna, Departamento de Análisis Matemático, 38271 La Laguna, Tenerife, Spain;Universidad de La Laguna, Departamento de Análisis Matemático, 38271 La Laguna, Tenerife, Spain;Universidad Complutense de Madrid, Departamento de Matemática Aplicada, 28040 Madrid, Spain
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 3
Cited 0

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Special polynomials and fractional calculus

Mathematical and Computer Modelling: An International Journal

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Abstract

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.