## Abstract

Two approaches for defining fractional derivatives of periodic distributions

are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Gr¨unwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotient. The equivalence of the two approaches is established and an application to a fractional diffusion equation, posed in a space of periodic distributions, is also discusse

are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Gr¨unwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotient. The equivalence of the two approaches is established and an application to a fractional diffusion equation, posed in a space of periodic distributions, is also discusse

Original language | English |
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Pages (from-to) | 260-283 |

Number of pages | 24 |

Journal | Fractional Calculus and Applied Analysis |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

## Keywords

- fractional derivatives
- distributions
- fractional integrals