TY - JOUR
ID - 7148
TI - Approximate solution of the fuzzy fractional Bagley-Torvik equation by the RBF collocation method
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Esmaeilbeigi, Mohsen
AU - Paripour, Mahmoud
AU - Garmanjani, Gholamreza
AD - Department of Mathematics, Faculty of Mathematics Science and Statistics,
Malayer University, Malayer 65719-95863, Iran
AD - Department of Computer Engineering and Information Technology,
Hamedan University of Technology, Hamedan 65155-579, Iran
Y1 - 2018
PY - 2018
VL - 6
IS - 2
SP - 186
EP - 214
KW - The fractional Bagley Torvik equation
KW - Meshless method
KW - RBF collocation
KW - Thin plate splines
KW - Fuzzy Caputo's H-differentiability
DO -
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_7148.html
L1 - https://cmde.tabrizu.ac.ir/article_7148_a8e2799dc7b6c1ad8b3e71b41bd5eaa6.pdf
ER -