Groundwater flow: new models for leaky and self-similar leaky aquifers with nonlocal differential operators - Mmanthupi, Ramotsho Amanda (University of the Free State, 2020)
During 2018 Ramotsho and Atangana published the article with the following title: “Derivation of a groundwater flow model within leaky and self-similar aquifers: Beyond Hantush model”. The scope of the work covered the explanation and background of leaky aquifers, existing equations, failure to apply the existing equations, derivation of the new generalized equation which represents the flow of groundwater in a leaky aquifer, introduction of self-similar leaky aquifers and the two derived equations. The conception of heterogeneity was covered in the article; however, the concept of memory effect and long term interaction was omitted. The proposed scope of this thesis is to introduce the three concepts of which are exponential law, Mittag Leffler law and power law into the new generalized equation, which represents the flow of water in a leaky aquifer. It has been proven in literature that the concept of fractional differentiation is well accounted for in nature and in the field. In chapter six, fractal-fractional operators are introduced and furthermore the different new numerical operators with different fractional operators are presented. The concept of fractal-fractional operators is introduced into the two equations for water flowing within a self-similar leaky aquifer. The results are presented in terms of simulations, where cone of depression figures against time or space are given. It has been depicted that as the order is increased the cone of depression decreases. This represents the real-life scenario or concept of permeability. The figures have been fully analyzed in chapter ten.
Thesis (Ph.D. (Geohydrology))--University of the Free State, 2020
Keywords: Ground-water management; Groundwater - Pollution