On Differential Equations With Indefinite Principal Parts

This doctoral dissertation consists of three refereed open access papers. These papers comprise chapters 2-4 herein. They deal with problems arising from a study of various differential equations with indefinite principal parts whether they be classified as ordinary, abstract, or fractional. In the first paper (Chapter 2) we show that Sturm’s separation theorem always fails for a classical real two term second order differential equation in the event that the principal part has one turning point inside the interval of definition. In the second paper (Chapter 3) we consider differential equations defined by so-called conformable derivatives and show that these differential operators are essentially multiplication operators (by a possibly sign-indefinite leading term) on a space of ordinary derivatives of functions. In the third paper (Chapter 4) we prove existence and uniqueness theorems for initial value problems and two-point boundary problems associated with fractional differential equations defined by composition of right Caputo differential operators and left Riemann-Liouville differential operators with indefinite principal parts.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Applied Mathematics

Grantor dc:publisher

Carleton University

Year dc:date.issued

2024

Author dc:creator

• Gholizadeh Zivlaei, Leila

Statement dc:rights

• Copyright © 2024 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, distribution to students, research and scholarship. Theses may only be shared by linking to the Carleton University Institutional Repository and no part may be copied without proper attribution to the author; no part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.

Language dc:language.iso

en

DOI

10.22215/etd/2024-16095

OAI identifier oai:identifier

oai:carleton.scholaris.ca:20.500.14718/43289