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...

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書目詳細資料
Main Authors: Salahshour, Soheil, Ahmadian, Ali, Senu, Norazak, Baleanu, Dumitru, Agarwal, Praveen
格式: Article
語言:English
出版: MDPI 2015
在線閱讀:http://psasir.upm.edu.my/id/eprint/56963/1/56963.pdf
實物特徵
總結: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.