# fractional calculus

The idea of calculus in fractional order is nearly as old as its integer counterpart. In a letter dated September 30th 1650, l’Hôpital posed the question of the meaning of $\frac{{d}^{\alpha}f}{d{x}^{\alpha}}$ if $\alpha ={\displaystyle \frac{1}{2}}$ to Leibniz.
There are different approaches to define calculus of fractional order. The following approaches are the most common and we can prove that they are equivalent^{}

(1) Riemann-Liouville approach of fractional integration

(2) Grunwald-Letnikov approach of fractional differentiation

Title | fractional calculus^{} |
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Canonical name | FractionalCalculus |

Date of creation | 2013-03-22 16:18:27 |

Last modified on | 2013-03-22 16:18:27 |

Owner | bchui (10427) |

Last modified by | bchui (10427) |

Numerical id | 14 |

Author | bchui (10427) |

Entry type | Definition |

Classification | msc 28B20 |

Synonym | fractional calculus |

Defines | fractional calculus |