In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.
","abstract_html":"<p>In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.</p>","abstract_has_math":false,"creators":["Pathak, Nimishaben Shailesh"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Sullivan, Michael"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-01T07:00:00Z","date_published":"2016-08-01T07:00:00Z","updated_at":"2026-07-24T04:35:08Z","subjects":["fractional derivative","Green’s function","Hilfer derivative","Laplace transforms","Lyapunov inequality","Mittag-Leffler function"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/1249","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Sullivan, Michael"]},{"key":"dc:creator","label":"Author","values":["Pathak, Nimishaben Shailesh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-08-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["fractional derivative","Green’s function","Hilfer derivative","Laplace transforms","Lyapunov inequality","Mittag-Leffler function"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/1249"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.
"]},{"key":"dc:title","label":"Title","values":["Lyapunov-type inequality and eigenvalue estimates for fractional problems"]}]}],"canonical_facts":{"dc:contributor":["Sullivan, Michael"],"dc:creator":["Pathak, Nimishaben Shailesh"],"dc:date.available":["2016-08-01T07:00:00Z"],"dc:description.abstract":["In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.
"],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/1249"],"dc:subject":["fractional derivative","Green’s function","Hilfer derivative","Laplace transforms","Lyapunov inequality","Mittag-Leffler function"],"dc:title":["Lyapunov-type inequality and eigenvalue estimates for fractional problems"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:35:08Z"}