In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions.
","abstract_html":"<p>In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions. </p>","abstract_has_math":false,"creators":["Hollon, Christina Ashley"],"institution":"Eastern Kentucky University","degree_name":"Master of Science (MS)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:25Z","subjects":["boundary value problems","differential equations","fractional calculus","Krasnoselskii","leggett williams","two-point","Mathematics"],"languages":[],"rights":["Copyright 2015 Christina Ashley Hollon"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/276","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hollon, Christina Ashley"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-07-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["boundary value problems","differential equations","fractional calculus","Krasnoselskii","leggett williams","two-point","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Christina Ashley Hollon"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/276"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions.
"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["Encompass Digital Archive: Online Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Existence of Positive Solutions to a Family of Fractional Two-Point Boundary Value Problems"]}]}],"canonical_facts":{"dc:creator":["Hollon, Christina Ashley"],"dc:date.available":["2016-07-01T07:00:00Z"],"dc:description.abstract":["In this paper we will consider an nth order fractional boundary value problem with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green's Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader's, Krasnozel'skii's, and Legget-Williams fixed point theorems to prove the existence of positive solutions under different conditions.
"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/276"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2015 Christina Ashley Hollon"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["boundary value problems","differential equations","fractional calculus","Krasnoselskii","leggett williams","two-point","Mathematics"],"dc:title":["Existence of Positive Solutions to a Family of Fractional Two-Point Boundary Value Problems"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MS)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:25Z"}