Applications of fractional calculus in Laplace transform theory

dc.contributor.advisorDenman, Eugene D.
dc.contributor.committeeMemberPaskusz, Gerhard F.
dc.contributor.committeeMemberCollins, R. Eugene
dc.creatorWhipple, Richard B.
dc.date.accessioned2022-07-29T17:49:35Z
dc.date.available2022-07-29T17:49:35Z
dc.date.issued1971
dc.description.abstractIn the study of Laplace transforms, the need sometimes arises to calculate a transform or inverse transform involving variables of non-integer order. The integral definitions of the Laplace transform can always be used directly but the required integration is sometimes rather difficult to carry out. When the variables involved are of integer order, a number of convenient operational techniques are available to aid in calculation. The purpose of this thesis is to generalize certain of these techniques so that application is possible to non-integer order variables. Before extending the methods of handling Laplace transforms, it is necessary to introduce the concept of fractional calculus. Since the subject is not widely known, a part of this thesis is concerned with providing the background material necessary to develop the Laplace transform extensions. Included is a historical review of fractional calculus along with a presentation of certain methods which can be used to calculate fractional derivatives and integrals for several specific functions. Finally, certain theorems of Laplace transform theory are modified to encompass the concepts of fractional calculus. These theorems are then applied to several example problems to demonstrate their usefulness.
dc.description.departmentElectrical and Computer Engineering, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13869102
dc.identifier.urihttps://hdl.handle.net/10657/10650
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleApplications of fractional calculus in Laplace transform theory
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Engineering
thesis.degree.departmentElectrical Engineering, Department of
thesis.degree.disciplineElectrical Engineering
thesis.degree.grantorUniversity of Houston
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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