Solution of Fractional Differential Equations: Transform and Iterative Methods Approach
A Master of Science thesis in Mathematics by Razan Abdul Satar Alchikh entitled, “Solution of Fractional Differential Equations: Variational Iteration Approachs”, submitted in December 2019. Thesis advisor is Dr. Suheil Khoury. Soft copy is available (Thesis, Approval Signatures, Completion Certific...
محفوظ في:
| المؤلف الرئيسي: | |
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| التنسيق: | doctoralThesis |
| منشور في: |
2019
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16645 |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513442927345664 |
|---|---|
| author | Alchikh, Razan Abdul Satar |
| author_facet | Alchikh, Razan Abdul Satar |
| author_role | author |
| dc.contributor.none.fl_str_mv | Khoury, Suheil A. |
| dc.creator.none.fl_str_mv | Alchikh, Razan Abdul Satar |
| dc.date.none.fl_str_mv | 2019-12 2020-03-01T07:16:51Z 2020-03-01T07:16:51Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2019.05 http://hdl.handle.net/11073/16645 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Fractional derivatives Fractional integration Caputo fractional derivative Liouville fractional derivative Green’s function Fixed-point iteration schemes Laplace transform |
| dc.title.none.fl_str_mv | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Razan Abdul Satar Alchikh entitled, “Solution of Fractional Differential Equations: Variational Iteration Approachs”, submitted in December 2019. Thesis advisor is Dr. Suheil Khoury. Soft copy is available (Thesis, Approval Signatures, Completion Certificate, and AUS Archives Consent Form). |
| format | doctoralThesis |
| id | aus_7be7c162e4935fc25e1665bd5f39d92f |
| identifier_str_mv | 29.232-2019.05 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16645 |
| publishDate | 2019 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Solution of Fractional Differential Equations: Transform and Iterative Methods ApproachAlchikh, Razan Abdul SatarFractional derivativesFractional integrationCaputo fractional derivativeLiouville fractional derivativeGreen’s functionFixed-point iteration schemesLaplace transformA Master of Science thesis in Mathematics by Razan Abdul Satar Alchikh entitled, “Solution of Fractional Differential Equations: Variational Iteration Approachs”, submitted in December 2019. Thesis advisor is Dr. Suheil Khoury. Soft copy is available (Thesis, Approval Signatures, Completion Certificate, and AUS Archives Consent Form).Fractional calculus is a novel and highly active area of research in the literature as it has a wide spectrum of applications in the physical sciences and engineering. In this thesis, we study the numerical solution of fractional differential equations subject to initial or boundary conditions. We employ two iterative methods for the solution of such equations. First, we implement a Laplace decomposition method (LDM) which is a combination of two methods: Laplace transform and a decomposition scheme. The nonlinear term is decomposed and a recursive algorithm is composed for the determination of the proposed infinite series solution. Second, we present another iterative technique that is based on the incorporation of Green’s functions into well-established fixed-point iterations, including Krasnoselskii-Mann’s and Picard’s schemes. Numerical experiments are conducted to demonstrate the efficiency, accuracy and applicability of the proposed methods, and then, to compare them with other schemes. In addition, we present graphs to understand the behavior of the numerical solutions. A patching strategy, based on domain decomposition, is suggested to overcome a deficiency of the LDM. Fractional differential equations are widely investigated by several researchers.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Khoury, Suheil A.2020-03-01T07:16:51Z2020-03-01T07:16:51Z2019-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2019.05http://hdl.handle.net/11073/16645en_USoai:repository.aus.edu:11073/166452025-06-26T12:30:44Z |
| spellingShingle | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach Alchikh, Razan Abdul Satar Fractional derivatives Fractional integration Caputo fractional derivative Liouville fractional derivative Green’s function Fixed-point iteration schemes Laplace transform |
| status_str | publishedVersion |
| title | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| title_full | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| title_fullStr | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| title_full_unstemmed | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| title_short | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| title_sort | Solution of Fractional Differential Equations: Transform and Iterative Methods Approach |
| topic | Fractional derivatives Fractional integration Caputo fractional derivative Liouville fractional derivative Green’s function Fixed-point iteration schemes Laplace transform |
| url | http://hdl.handle.net/11073/16645 |