Symmetry and conservation laws of recurrence equations and classes of time-fractional equations
Date
2021
Authors
Mnguni, Nkosingiphile
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The thesis focuses on the symmetry analysis of two types of equation classes. The
first part of the thesis involves the novel study of symmetry analysis on classes of
time-fractional partial differential equations. Firstly, a Lie group analysis method
is used to obtain the solutions of fractional-order population growth models, where
a time component is defined by Riemann-Liouville derivative. Furthermore, the Lie
group analysis is extended to the time-fractional axisymmetric spreading of a thin
incompressible power-law fluid on a horizontal plane. The solutions and their graph ical representation are obtained. The second part of the thesis involves the study
of symmetries to find the exact solutions of recurrence equations. We investigate
the symmetry analysis on some fourth, fifth and sixth order recurrence equations
and obtain their respective solutions for special cases of the recurrence equations.
Furthermore this analysis is extended to a general k+1-th order recurrence equation
Description
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2021