{"id":{"repo_id":"eku","oai_identifier":"oai:encompass.eku.edu:etd-1387"},"canonical_url":"https://search.dev.ndltd.org/etd/eku/oai:encompass.eku.edu:etd-1387","repository":{"repo_id":"eku","name":"Eastern Kentucky University","base_url":"https://encompass.eku.edu/do/oai/"},"display":{"title":"Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition","abstract":"<p>We establish the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0< t< 1, satisfying the boundary conditions when n-1<α≤ n. First, we consider the case when 0<β<n-1, satisfying u^(i) (0)=0, i=0,1,…,n-2,D_(0^+)^β u(1)=0. Then, the case when β=0 is considered, satisfying the conditions u^(i)(0)=0, for i=0,1,…,n-2, and u(1)=0. </p>","abstract_html":"&lt;p&gt;We establish the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0&lt; t&lt; 1, satisfying the boundary conditions when n-1&lt;α≤ n. First, we consider the case when 0&lt;β&lt;n-1, satisfying u^(i) (0)=0, i=0,1,…,n-2,D_(0^+)^β u(1)=0. Then, the case when β=0 is considered, satisfying the conditions u^(i)(0)=0, for i=0,1,…,n-2, and u(1)=0. &lt;/p&gt;","abstract_has_math":false,"creators":["Koester, Angela"],"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":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:32Z","subjects":["eigenvalues","fractional boundary conditions","fractional boundary value problem","Algebra"],"languages":[],"rights":["Copyright 2016 Angela Koester"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/389","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Koester, Angela"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"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":["eigenvalues","fractional boundary conditions","fractional boundary value problem","Algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Angela Koester"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/389"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We establish the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0< t< 1, satisfying the boundary conditions when n-1<α≤ n. First, we consider the case when 0<β<n-1, satisfying u^(i) (0)=0, i=0,1,…,n-2,D_(0^+)^β u(1)=0. Then, the case when β=0 is considered, satisfying the conditions u^(i)(0)=0, for i=0,1,…,n-2, and u(1)=0. </p>"]},{"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":["Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition"]}]}],"canonical_facts":{"dc:creator":["Koester, Angela"],"dc:description.abstract":["<p>We establish the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0< t< 1, satisfying the boundary conditions when n-1<α≤ n. First, we consider the case when 0<β<n-1, satisfying u^(i) (0)=0, i=0,1,…,n-2,D_(0^+)^β u(1)=0. Then, the case when β=0 is considered, satisfying the conditions u^(i)(0)=0, for i=0,1,…,n-2, and u(1)=0. </p>"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/389"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2016 Angela Koester"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["eigenvalues","fractional boundary conditions","fractional boundary value problem","Algebra"],"dc:title":["Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition"],"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":"2026-07-24T02:15:32Z"}