Boundary value problems of nabla fractional difference equations.

机译：Nabla分数差分方程的边值问题。

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In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation. We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

机译：在本文中，我们发展了nabla分数自伴差方程的理论。我们首先介绍纳布拉分数微积分。在第二章中，我们展示了分数自伴初始值问题解的存在性和唯一性。我们找到了这个分数初值问题的常数公式的变化，并使用常数公式的变化来推导相关边值问题的格林函数。我们在几种设置下研究Green的功能及其属性。对于简化的边值问题，我们表明格林函数是非负的，我们找到了它的最大值和其积分的最大值。对于具有广义边界条件的边值问题，我们找到了格林函数，并证明它是第一个格林函数的推广。在第三章中，我们使用压缩映射定理证明了一个有限极限的强迫自伴分数差分方程正解的存在性和唯一性。我们探索对强迫项的修改以及对存在解决方案的函数空间的修改，并提供示例来演示这些定理的用法。

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作者
Brackins, Abigail.;
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作者单位

The University of Nebraska - Lincoln.;

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授予单位 The University of Nebraska - Lincoln.;
学科 Mathematics.
学位 Ph.D.
年度 2014
页码 92 p.
总页数 92
原文格式 PDF
正文语种 eng
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8. Hybrid Difference Methods for the Initial Boundary-Value Problem for Hyperbolic Equations. [R] . oliger, j. 2001

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Boundary value problems of nabla fractional difference equations.

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