### Abstract

This paper considers the approximations of three classes of fractional derivatives (FD) using modified Gauss integration (MGI) and Gauss-Laguerre integration (GLI). The main solutions of these fractional derivatives depend on the inverse of Laplace transforms, which are handled by these procedures. In the modified form of the integration, the weights and nodes are obtained by means of a difference equation that, gives a proper approximation form for the inverse of Laplace transform and hence the fractional derivatives. Theorems are established to indicate the degree of exactness and boundary of the error of the solutions. Numerical examples are given to illuminate the results of the application of these methods.

Original language | English |
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Pages (from-to) | 67-87 |

Number of pages | 21 |

Journal | Annali dell'Universita di Ferrara |

Volume | 57 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 2011 |

Externally published | Yes |

### Keywords

- Fractional derivative
- Gauss quadrature
- Laplace transform

## Cite this

*Annali dell'Universita di Ferrara*,

*57*(1), 67-87. https://doi.org/10.1007/s11565-011-0120-x