{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/21696"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/21696","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"Fractional Diffusion in Gaussian Noisy Environment","abstract":"Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel.","abstract_html":"Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel.","abstract_has_math":false,"creators":["Hu, Guannan"],"institution":"University of Kansas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Hu, Yaozhong"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-12-31","date_published":"2015-12-31","updated_at":"2026-07-24T02:46:17Z","subjects":["Mathematics","chaos expansion","Fox's H-function;","fractional derivative","Green's functions","mild solution","multiple integral of the Itô type"],"languages":["en"],"rights":["Copyright held by the author."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://dissertations.umi.com/ku:14276"],"render_values":[{"text":"http://dissertations.umi.com/ku:14276","href":"http://dissertations.umi.com/ku:14276","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1808/21696","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hu, Yaozhong"]},{"key":"dc:creator","label":"Author","values":["Hu, Guannan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-10-12T02:39:26Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-10-12T02:39:26Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-12-31"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","chaos expansion","Fox's H-function;","fractional derivative","Green's functions","mild solution","multiple integral of the Itô type"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright held by the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["http://dissertations.umi.com/ku:14276"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1808/21696"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel."]},{"key":"dc:title","label":"Title","values":["Fractional Diffusion in Gaussian Noisy Environment"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hu, Yaozhong"],"dc:creator":["Hu, Guannan"],"dc:date.accessioned":["2016-10-12T02:39:26Z"],"dc:date.available":["2016-10-12T02:39:26Z"],"dc:date.issued":["2015-12-31"],"dc:description.abstract":["Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate the moment bounds of the solution when the noise has Reisz kernel as space covariance. Along the way, we obtain some new properties of the fundamental solutions. Chapter 4 studies the time-fractional diffusion with fractional Gaussian noise. We obtain conditions so that the square integrable solution exists uniquely. Chapter 5 studies the time-fractional diffusion where the Gaussian noise is general in time with space covariance given by fractional, Riesz and Bessel kernel."],"dc:identifier.other":["http://dissertations.umi.com/ku:14276"],"dc:identifier.uri":["http://hdl.handle.net/1808/21696"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:rights":["Copyright held by the author."],"dc:subject":["Mathematics","chaos expansion","Fox's H-function;","fractional derivative","Green's functions","mild solution","multiple integral of the Itô type"],"dc:title":["Fractional Diffusion in Gaussian Noisy Environment"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:46:17Z"}