Honors Theses

Author(s)

Tyler Masthay

Advisor

Paul Eloe, Ph.D.

Department

Mathematics

Publication Date

4-2017

Document Type

Honors Thesis

Abstract

In 1967, Andrzej Lasota and Zdzisław Opial proved that under sufficient conditions, uniqueness of solutions for boundary value problems for a second-order ordinary differential equation implies their existence. Lloyd Jackson and Keith Schrader then proved an extension of this result for boundary value problems of third order. In proving the third-order case, this compactness theorem is applied as a key part of the proof. It states that under sufficient conditions, uniform boundedness of a sequence of solutions on a compact domain implies existence of a subsequence which converges uniformly with respect to its zeroth, first, and second derivatives. We present an extension of this compactness theorem to a fractional differential equation of all orders in the interval (2,3].

Permission Statement

This item is protected by copyright law (Title 17, U.S. Code) and may only be used for noncommercial, educational, and scholarly purposes

Disciplines

Mathematics | Physical Sciences and Mathematics


Included in

Mathematics Commons

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