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Approximate solution of the fuzzy fractional Bagley-Torvik equation by the RBF collocation method | ||
| Computational Methods for Differential Equations | ||
| مقاله 6، دوره 6، شماره 2، تیر 2018، صفحه 186-214 اصل مقاله (1.04 M) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Mohsen Esmaeilbeigi1؛ Mahmoud Paripour* 2؛ Gholamreza Garmanjani1 | ||
| 1Department of Mathematics, Faculty of Mathematics Science and Statistics, Malayer University, Malayer 65719-95863, Iran | ||
| 2Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan 65155-579, Iran | ||
| چکیده | ||
| In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< \nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $\nu$ ($1< \nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. The main advantage of this approach is that the fuzzy fractional Bagley-Torvik equation is reduced to the problem of solving two systems of linear equations. Determining a good shape parameter is still an outstanding research topic. To eliminate the effects of the radial basis function shape parameter, we use thin plate spline radial basis functions which have no shape parameter. The numerical investigation is presented in this paper shows that excellent accuracy can be obtained even when few nodes are used in analysis. Efficiency and effectiveness of the proposed procedure is examined by solving two benchmark problems. | ||
| کلیدواژهها | ||
| The fractional Bagley Torvik equation؛ Meshless method؛ RBF collocation؛ Thin plate splines؛ Fuzzy Caputo's H-differentiability | ||
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