Mean-square fractional calculus and some applications.

Institution: | University of KwaZulu-Natal |
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Department: | Statistics |

Year: | 2015 |

Keywords: | Statistics. |

Record ID: | 1481129 |

Full text PDF: | http://hdl.handle.net/10413/11790 |

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.