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dc.contributor.advisorRazzaghi, Mohsen
dc.contributor.authorMashayekhi, Somayeh
dc.date2015
dc.date.accessioned2020-09-10T21:53:48Z
dc.date.available2020-09-10T21:53:48Z
dc.identifier.urihttps://hdl.handle.net/11668/19772
dc.description.abstractIn this dissertation, a new numerical method for solving the fractional dynamical systems, is presented. We first introduce Riemann-Liouville fractional integral operator for hybrid functions. Then we will show the spectral accuracy of the present method for solving fractional-order differential equations, and we will extend the present method for solving nonlinear fractional integro-differential equations, fractional Bagley-Torvik equation, distributed order fractional differential equations, two-dimensional fractional partial differential equations, and fractional optimal control problems. In all cases, we will show the rate of convergence is more than some existing numerical methods which were used to solve these kind of problems in the literature. Illustrative examples are included to demonstrate the validity and applicability of the technique.
dc.publisherMississippi State University
dc.subject.otherHybrid functions
dc.subject.otherfractional-order differential equations
dc.subject.otherblock-pulse
dc.subject.otherCaputo derivative
dc.subject.othernumerical solution
dc.subject.otherBernoulli polynomials
dc.titleHybrid functions in Fractional Calculus
dc.typeDissertation
dc.publisher.departmentDepartment of Mathematics and Statistics
dc.publisher.collegeCollege of Arts & Science
dc.date.authorbirth1980
dc.subject.degreeDoctor of Philosophy
dc.contributor.committeeQian, Chuanxi
dc.contributor.committeeJohnson, Corlis P.
dc.contributor.committeeKim, Seongjai
dc.contributor.committeeYarahmadian, Shantia
dc.contributor.committeeMiller, T. Len


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