Symmetry and conservation laws of recurrence equations and classes of time-fractional equations

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dc.contributor.authorMnguni, Nkosingiphile
dc.date.accessioned2021-12-18T20:55:04Z
dc.date.available2021-12-18T20:55:04Z
dc.date.issued2021
dc.descriptionA 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, 2021en_ZA
dc.description.abstractThe 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 equationen_ZA
dc.description.librarianTL (2021)en_ZA
dc.facultyFaculty of Scienceen_ZA
dc.identifier.urihttps://hdl.handle.net/10539/32446
dc.language.isoenen_ZA
dc.phd.titlePHDen_ZA
dc.schoolSchool of Mathematicsen_ZA
dc.titleSymmetry and conservation laws of recurrence equations and classes of time-fractional equationsen_ZA
dc.typeThesisen_ZA
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