Symmetry and conservation laws of recurrence equations and classes of time-fractional equations - Mnguni, Nkosingiphile (My University, 2021)
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
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