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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| Format: | Thesis |
| Language: | English |
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2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf |
| _version_ | 1825949883789475840 |
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| author | Ahmood, Wasan Ajeel |
| author_facet | Ahmood, Wasan Ajeel |
| author_sort | Ahmood, Wasan Ajeel |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T10:06:07Z |
| format | Thesis |
| id | upm.eprints-70908 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:06:07Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | upm.eprints-709082019-08-07T04:43:24Z http://psasir.upm.edu.my/id/eprint/70908/ Extension of laplace transform to multi-dimensional fractional integro-differential equations 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. 2017-05 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf Ahmood, Wasan Ajeel (2017) Extension of laplace transform to multi-dimensional fractional integro-differential equations. Doctoral thesis, Universiti Putra Malaysia. Laplace transformation |
| spellingShingle | Laplace transformation Ahmood, Wasan Ajeel Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title | 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_short | Extension of laplace transform to multi-dimensional fractional integro-differential equations |
| title_sort | extension of laplace transform to multi dimensional fractional integro differential equations |
| topic | Laplace transformation |
| url | http://psasir.upm.edu.my/id/eprint/70908/1/FS%202017%2042%20IR.pdf |
| work_keys_str_mv | AT ahmoodwasanajeel extensionoflaplacetransformtomultidimensionalfractionalintegrodifferentialequations |