Extension of laplace transform to multi-dimensional fractional integro-differential equations
The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional cal...
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2017
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my-upm-ir.709082019-08-07T04:43:24Z Extension of laplace transform to multi-dimensional fractional integro-differential equations 2017-05 Ahmood, Wasan Ajeel The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional calculus such as space-time partial fractional derivative. The multi-dimensional Laplace transforms method used to solve the multi-dimensional fractional calculus with constant and variable coefficients and the multidimensional modification of Hes variational iteration method to solve the multi-dimensional fractional integro-differential equations with non-local boundary conditions are developed. The study of multi-dimensional space-time fractional derivative with their applications and also, new fractional derivative and integral including Riemann-Liouville having a non-local and non-singular kernel are detailed. Finally, we obtained the exact solution of multi-dimensional fractional calculus, space-time partial fractional derivative and the system of matrix fractional differential equation in Riemann- Liouville sense of matrices but there are some problems that cannot be solved analytically, thus we solved them by multi-dimensional variational iteration method. This study shows that integral transform can be used to present new solutions to problems by certain applications for solving them. Laplace transformation 2017-05 Thesis http://psasir.upm.edu.my/id/eprint/70908/ http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf text en public doctoral Universiti Putra Malaysia Laplace transformation |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English |
| topic |
Laplace transformation |
| spellingShingle |
Laplace transformation Ahmood, Wasan Ajeel Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| description |
The main focus of this thesis is to extend the study of one-dimensional fractional to multi-dimensional fractional calculus and study of multi-dimensional Laplace transformation with their respective applications. This extension will be used to solve special types of multi-dimensional fractional calculus such as space-time partial fractional derivative. The multi-dimensional Laplace transforms method used to solve the multi-dimensional fractional calculus with constant and variable coefficients and the multidimensional modification of Hes variational iteration method to solve the multi-dimensional fractional integro-differential equations with non-local boundary conditions are developed. The study of multi-dimensional space-time fractional derivative with their applications and also, new fractional derivative and integral including Riemann-Liouville having a non-local and non-singular kernel are detailed. Finally, we obtained the exact solution of multi-dimensional fractional calculus, space-time partial fractional derivative and the system of matrix fractional differential equation in Riemann- Liouville sense of matrices but there are some problems that cannot be solved analytically, thus we solved them by multi-dimensional variational iteration method. This study shows that integral transform can be used to present new solutions to problems by certain applications for solving them. |
| format |
Thesis |
| qualification_level |
Doctorate |
| author |
Ahmood, Wasan Ajeel |
| author_facet |
Ahmood, Wasan Ajeel |
| author_sort |
Ahmood, Wasan Ajeel |
| title |
Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_short |
Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_full |
Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_fullStr |
Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_full_unstemmed |
Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_sort |
extension of laplace transform to multi-dimensional fractional integro-differential equations |
| granting_institution |
Universiti Putra Malaysia |
| publishDate |
2017 |
| url |
http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf |
| _version_ |
1747812933937659904 |