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.
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