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dc.contributor.advisorKhoury, Suheil A.
dc.contributor.authorAlchikh, Razan Abdul Satar
dc.date.accessioned2020-03-01T07:16:51Z
dc.date.available2020-03-01T07:16:51Z
dc.date.issued2019-12
dc.identifier.other29.232-2019.05
dc.identifier.urihttp://hdl.handle.net/11073/16645
dc.descriptionA 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).en_US
dc.description.abstractFractional 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.en_US
dc.description.sponsorshipCollege of Arts and Sciencesen_US
dc.description.sponsorshipDepartment of Mathematics and Statisticsen_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesAmerican University of Sharjah Student Worken_US
dc.relation.ispartofseriesMaster of Science in Mathematics (MSMTH)en_US
dc.subjectFractional derivativesen_US
dc.subjectFractional integrationen_US
dc.subjectCaputo fractional derivativeen_US
dc.subjectLiouville fractional derivativeen_US
dc.subjectGreen’s functionen_US
dc.subjectFixed-point iteration schemesen_US
dc.subjectLaplace transformen_US
dc.titleSolution of Fractional Differential Equations: Transform and Iterative Methods Approachen_US
dc.typeThesisen_US


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