On some applications of the space-time fractional derivative
In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf |
| _version_ | 1825930851305652224 |
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| author | Ahmood, Wasan Ajeel Kilicman, Adem |
| author_facet | Ahmood, Wasan Ajeel Kilicman, Adem |
| author_sort | Ahmood, Wasan Ajeel |
| collection | UPM |
| description | In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional derivative is developed to augment the equations. The results show that this method is effective, convenient, and easily executable. The main advantage of the proposed approach is that it is an accurate analytical method (the Laplace transform method) that can be implemented for both space and time discretizations of the fractional derivatives and allows us to present new solutions to problems by certain applications for solving space-time fractional derivatives. |
| first_indexed | 2024-03-06T09:17:50Z |
| format | Article |
| id | upm.eprints-53429 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:17:50Z |
| publishDate | 2016 |
| publisher | SpringerOpen |
| record_format | dspace |
| spelling | upm.eprints-534292017-10-30T08:01:59Z http://psasir.upm.edu.my/id/eprint/53429/ On some applications of the space-time fractional derivative Ahmood, Wasan Ajeel Kilicman, Adem In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional derivative is developed to augment the equations. The results show that this method is effective, convenient, and easily executable. The main advantage of the proposed approach is that it is an accurate analytical method (the Laplace transform method) that can be implemented for both space and time discretizations of the fractional derivatives and allows us to present new solutions to problems by certain applications for solving space-time fractional derivatives. SpringerOpen 2016-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf Ahmood, Wasan Ajeel and Kilicman, Adem (2016) On some applications of the space-time fractional derivative. Advances in Difference Equations, 2016 (1). pp. 1-14. ISSN 1687-1839; ESSN: 1687-1847 https://link.springer.com/article/10.1186/s13662-016-1015-z 10.1186/s13662-016-1015-z |
| spellingShingle | Ahmood, Wasan Ajeel Kilicman, Adem On some applications of the space-time fractional derivative |
| title | On some applications of the space-time fractional derivative |
| title_full | On some applications of the space-time fractional derivative |
| title_fullStr | On some applications of the space-time fractional derivative |
| title_full_unstemmed | On some applications of the space-time fractional derivative |
| title_short | On some applications of the space-time fractional derivative |
| title_sort | on some applications of the space time fractional derivative |
| url | http://psasir.upm.edu.my/id/eprint/53429/1/On%20some%20applications%20of%20the%20space-time.pdf |
| work_keys_str_mv | AT ahmoodwasanajeel onsomeapplicationsofthespacetimefractionalderivative AT kilicmanadem onsomeapplicationsofthespacetimefractionalderivative |