On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem
In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional deriv...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56963/1/56963.pdf |
| _version_ | 1825931519152095232 |
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| author | Salahshour, Soheil Ahmadian, Ali Senu, Norazak Baleanu, Dumitru Agarwal, Praveen |
| author_facet | Salahshour, Soheil Ahmadian, Ali Senu, Norazak Baleanu, Dumitru Agarwal, Praveen |
| author_sort | Salahshour, Soheil |
| collection | UPM |
| description | In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method. |
| first_indexed | 2024-03-06T09:27:58Z |
| format | Article |
| id | upm.eprints-56963 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:27:58Z |
| publishDate | 2015 |
| publisher | MDPI |
| record_format | dspace |
| spelling | upm.eprints-569632017-09-06T09:34:50Z http://psasir.upm.edu.my/id/eprint/56963/ On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem Salahshour, Soheil Ahmadian, Ali Senu, Norazak Baleanu, Dumitru Agarwal, Praveen In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method. MDPI 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56963/1/56963.pdf Salahshour, Soheil and Ahmadian, Ali and Senu, Norazak and Baleanu, Dumitru and Agarwal, Praveen (2015) On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem. Entropy, 17 (2). pp. 885-902. ISSN 1099-4300 http://www.mdpi.com/1099-4300/17/2/885 10.3390/e17020885 |
| spellingShingle | Salahshour, Soheil Ahmadian, Ali Senu, Norazak Baleanu, Dumitru Agarwal, Praveen On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title | On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title_full | On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title_fullStr | On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title_full_unstemmed | On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title_short | On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem |
| title_sort | on analytical solutions of the fractional differential equation with uncertainty application to the basset problem |
| url | http://psasir.upm.edu.my/id/eprint/56963/1/56963.pdf |
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