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Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik
Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik
Masters Theses & Specialist Projects
This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental …
Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey
Masters Theses & Specialist Projects
In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the …
Boundary Problems For One And Two Dimensional Random Walks, Miky Wright
Boundary Problems For One And Two Dimensional Random Walks, Miky Wright
Masters Theses & Specialist Projects
This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …