A novel numerical method for solving autonomous initial value problems of fractional order differential equations

dc.contributor.advisorBagley, Ronald L.
dc.contributor.authorSuthangkornkul, Peeradech
dc.contributor.committeeMemberFeng, Yusheng
dc.contributor.committeeMemberMillwater, Harry
dc.date.accessioned2024-03-08T15:43:45Z
dc.date.available2024-03-08T15:43:45Z
dc.date.issued2011
dc.descriptionThis item is available only to currently enrolled UTSA students, faculty or staff. To download, navigate to Log In in the top right-hand corner of this screen, then select Log in with my UTSA ID.
dc.description.abstractDue to the recent growth of fractional calculus in many practical scientific problems, a new numerical method for solving autonomous initial value problems of fractional order differential equations is presented. This method is based on using a circular sampling technique with the Fourier transform to obtain the coefficients to construct an approximate solution to the problem in a form of Taylor series expansion. Laplace transform of fractional order integrals and Laplace transform of fractional order derivatives are used in the method. Since the process of this method is mainly performed by the substitution and the symbolic integration, there is no need to change in the body of the structure for any different problems in this type. The accuracy of the method can be adjusted in several ways. Moreover, the error due to the past time dependence in the present time calculation, which occurs in numerical methods for solving fractional order differential equations, does not appear in this solution method. In the end, the results illustrate that the approximate solutions can be within satisfactory criteria if the relevant parameters are properly chosen.
dc.description.departmentMechanical Engineering
dc.format.extent69 pages
dc.format.mimetypeapplication/pdf
dc.identifier.isbn9781124629025
dc.identifier.urihttps://hdl.handle.net/20.500.12588/5661
dc.languageen
dc.subjectFractional Calculus
dc.subjectFractional Differential Equations
dc.subjectHarmonic Analysis
dc.subjectInitial Value Problems
dc.subjectNumerical Method
dc.subjectPower-Fourier Series
dc.subject.classificationMathematics
dc.subject.classificationMechanical engineering
dc.titleA novel numerical method for solving autonomous initial value problems of fractional order differential equations
dc.typeThesis
dc.type.dcmiText
dcterms.accessRightspq_closed
thesis.degree.departmentMechanical Engineering
thesis.degree.grantorUniversity of Texas at San Antonio
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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