### Abstract

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

Language | English |
---|---|

Pages | 260-283 |

Number of pages | 24 |

Journal | Fractional Calculus and Applied Analysis |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- fractional derivatives
- distributions
- fractional integrals

### Cite this

*Fractional Calculus and Applied Analysis*,

*14*(2), 260-283. https://doi.org/10.2478/s13540-011-0016-6

}

*Fractional Calculus and Applied Analysis*, vol. 14, no. 2, pp. 260-283. https://doi.org/10.2478/s13540-011-0016-6

**Fractional calculus of periodic distributions.** / Khan, Khaula Naeem; Lamb, Wilson; Mcbride, Adam.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fractional calculus of periodic distributions

AU - Khan, Khaula Naeem

AU - Lamb, Wilson

AU - Mcbride, Adam

N1 - changed journal title

PY - 2011

Y1 - 2011

N2 - Two approaches for defining fractional derivatives of periodic distributionsare 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

AB - Two approaches for defining fractional derivatives of periodic distributionsare 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

KW - fractional derivatives

KW - distributions

KW - fractional integrals

U2 - 10.2478/s13540-011-0016-6

DO - 10.2478/s13540-011-0016-6

M3 - Article

VL - 14

SP - 260

EP - 283

JO - Fractional Calculus and Applied Analysis

T2 - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 2

ER -