dc.contributor.advisor | Dale, A. I. | |

dc.creator | Pitts, Susan. | |

dc.date.accessioned | 2015-01-05T06:57:21Z | |

dc.date.available | 2015-01-05T06:57:21Z | |

dc.date.created | 2012 | |

dc.date.issued | 2012 | |

dc.identifier.uri | http://hdl.handle.net/10413/11790 | |

dc.description | M. Sc. University of KwaZulu-Natal, Durban 2012. | en |

dc.description.abstract | The fractional calculus of deterministic functions is well known and
widely used. Mean-square calculus is a calculus that is suitable for use
when dealing with second-order stochastic processes. In this dissertation
we explore the idea of extending the fractional calculus of deterministic
functions to a mean-square setting. This exploration includes the development
of some of the theoretical aspects of mean-square fractional calculus
– such as definitions and properties – and the consideration of the application
of mean square fractional calculus to fractional random differential
and integral equations. The development of mean-square calculus follows
closely that of the calculus of deterministic functions making mean square
calculus more accessible to a large audience. Wherever possible, our development
of mean-square fractional calculus is done in a similar manner to
that of ordinary fractional calculus so as to make mean-square fractional
calculus more accessible to people with some exposure to ordinary fractional
calculus. | en |

dc.language.iso | en_ZA | en |

dc.subject | Fractional calculus. | en |

dc.subject | Fractional differential equations. | en |

dc.subject | Differential calculus. | en |

dc.subject | Fractional integrals. | en |

dc.subject | Stochastic processes. | en |

dc.subject | Differential equations. | en |

dc.subject | Theses--Statistics. | en |

dc.title | Mean-square fractional calculus and some applications. | en |

dc.type | Thesis | en |