Application of a spectral method to Fractional Differential Equations under uncertainty¹

Article type: Research Article

Authors: Sin, Kinam^{a; b} | Chen, Minghao^{a; *} | Wu, Chong^a | Ri, Kwang^{a; c} | Choi, Huichol^b

Affiliations: [a] Harbin Institute of Technology, Harbin, PR China | [b] Faculty of Mathematics, Kim Il Sung University, Pyongyang, D.P.R. of Korea | [c] Department of Applied Mathematics, Kim Chaek University of Technology, Pyongyang, D.P.R. of Korea

Correspondence: [*] Corresponding author. Minghao Chen. E-mail: chenmh130264@hit.edu.cn (M. Chen).

Note: [1] This work was supported by the National Natural Science Foundation of China (Grant Nos.11771111 and 11471088).

Abstract: The main result obtained in this paper is constructed the fractional Chebyshev operational matrix based on generalized shifted fractional-order Chebyshev functions of the first and second kind, is applied this operational matrix to the problem for numerically solving fuzzy fractional differential equations of order 0 < ν < 1 with fuzzy initial condition. We shown through numerical result that a new tau method is effective to the good approximate solution of Kelvin-Voiget equation, the model of viscosity behavior for non-Newtonian fluid and fuzzy fractional differential equation with variable coefficient. The numerical accuracy are compared with the results obtained by generalized fractional-order Legendre functions, Chebyshev polynomials and Jacobi polynomials.

Keywords: Fuzzy fractional differential equation, fractional Chebyshev operational matrix, Caputo-type fuzzy fractional derivative

DOI: 10.3233/JIFS-18732

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4821-4835, 2018