This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental definitions and formulas in discrete fractional calculus. In the third chapter, we introduce two new monotonicity concepts for nonnegative or nonpositive valued functions defined on discrete domains, and then we prove some monotonicity criteria based on the sign of the fractional difference operator of a function. In the fourth chapter, we emphasize the rheological models: We start by giving a brief introduction to rheological models such as Maxwell and Kelvin-Voigt, and then we construct and solve discrete fractional rheological constitutive equations. Finally, we finish this thesis by describing the conclusion and future work.
","abstract_html":"<p>This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental definitions and formulas in discrete fractional calculus. In the third chapter, we introduce two new monotonicity concepts for nonnegative or nonpositive valued functions defined on discrete domains, and then we prove some monotonicity criteria based on the sign of the fractional difference operator of a function. In the fourth chapter, we emphasize the rheological models: We start by giving a brief introduction to rheological models such as Maxwell and Kelvin-Voigt, and then we construct and solve discrete fractional rheological constitutive equations. Finally, we finish this thesis by describing the conclusion and future work.</p>","abstract_has_math":false,"creators":["Uyanik, Meltem"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics","degree_department":null,"school":null,"contributors":["Dr. Ferhan Atici (Director), Dr. Dominic Lanphier, and Dr. Mark Robinson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-05-01T07:00:00Z","date_published":"2015-05-01T07:00:00Z","updated_at":"2026-07-24T06:08:52Z","subjects":["Discrete fractional calculus","discrete forward operator","discrete fractional Maxwell model","discrete fractional Kelvin-Voight model","Discrete Mathematics and Combinatorics","Mathematics","Other Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/1491","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Ferhan Atici (Director), Dr. Dominic Lanphier, and Dr. Mark Robinson"]},{"key":"dc:creator","label":"Author","values":["Uyanik, Meltem"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Discrete fractional calculus","discrete forward operator","discrete fractional Maxwell model","discrete fractional Kelvin-Voight model","Discrete Mathematics and Combinatorics","Mathematics","Other Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/1491"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental definitions and formulas in discrete fractional calculus. In the third chapter, we introduce two new monotonicity concepts for nonnegative or nonpositive valued functions defined on discrete domains, and then we prove some monotonicity criteria based on the sign of the fractional difference operator of a function. In the fourth chapter, we emphasize the rheological models: We start by giving a brief introduction to rheological models such as Maxwell and Kelvin-Voigt, and then we construct and solve discrete fractional rheological constitutive equations. Finally, we finish this thesis by describing the conclusion and future work.
"]},{"key":"dc:title","label":"Title","values":["Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models"]}]}],"canonical_facts":{"dc:contributor":["Dr. Ferhan Atici (Director), Dr. Dominic Lanphier, and Dr. Mark Robinson"],"dc:creator":["Uyanik, Meltem"],"dc:description.abstract":["This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental definitions and formulas in discrete fractional calculus. In the third chapter, we introduce two new monotonicity concepts for nonnegative or nonpositive valued functions defined on discrete domains, and then we prove some monotonicity criteria based on the sign of the fractional difference operator of a function. In the fourth chapter, we emphasize the rheological models: We start by giving a brief introduction to rheological models such as Maxwell and Kelvin-Voigt, and then we construct and solve discrete fractional rheological constitutive equations. Finally, we finish this thesis by describing the conclusion and future work.
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