Mean-square fractional calculus and some applications.
| dc.contributor.advisor | Dale, Andrew Ian. | |
| dc.contributor.author | 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.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.identifier.uri | http://hdl.handle.net/10413/11790 | |
| 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 |