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University of Nebraska - Lincoln
Department of Mathematics: Dissertations, Theses, and Student Research
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Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch
Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch
Department of Mathematics: Dissertations, Theses, and Student Research
The purpose of this dissertation is to develop and apply results of both discrete calculus and discrete fractional calculus to further develop results on various discrete time scales. Two main goals of discrete and fractional discrete calculus are to extend results from traditional calculus and to unify results on the real line with those on a variety of subsets of the real line. Of particular interest is introducing and analyzing results related to a generalized fractional boundary value problem with Lidstone boundary conditions on a standard discrete domain N_a. We also introduce new results regarding exponential order for functions on …