Hybrid functions in fractional calculus
<p>In 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 differe...
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ndltd-MSSTATE-oai-library.msstate.edu-etd-05052015-1359172016-07-15T15:48:15Z Hybrid functions in fractional calculus Mashayekhi, Somayeh Mathematics and Statistics <p>In 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.</p> Seongjai Kim T. Len Miller Chuanxi Qian Shantia Yarahmadian Corlis P. Johnson Mohsen Razzaghi MSSTATE 2015-07-27 text application/pdf http://sun.library.msstate.edu/ETD-db/theses/available/etd-05052015-135917/ http://sun.library.msstate.edu/ETD-db/theses/available/etd-05052015-135917/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, Dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Mississippi State University Libraries or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, Dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, Dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, Dissertation, or project report. |
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Mathematics and Statistics Mashayekhi, Somayeh Hybrid functions in fractional calculus |
description |
<p>In 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.</p> |
author2 |
Seongjai Kim |
author_facet |
Seongjai Kim Mashayekhi, Somayeh |
author |
Mashayekhi, Somayeh |
author_sort |
Mashayekhi, Somayeh |
title |
Hybrid functions in fractional calculus |
title_short |
Hybrid functions in fractional calculus |
title_full |
Hybrid functions in fractional calculus |
title_fullStr |
Hybrid functions in fractional calculus |
title_full_unstemmed |
Hybrid functions in fractional calculus |
title_sort |
hybrid functions in fractional calculus |
publisher |
MSSTATE |
publishDate |
2015 |
url |
http://sun.library.msstate.edu/ETD-db/theses/available/etd-05052015-135917/ |
work_keys_str_mv |
AT mashayekhisomayeh hybridfunctionsinfractionalcalculus |
_version_ |
1718350101152268288 |