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In this paper the fuzzy Caputo fractional differential equation (FCFDE) under the Generalized Hukuhara differentiability is introduced. Also the existence and uniqueness of the solution for a class of fuzzy Caputo fractional differential equation with initial value is studied, and an analytical solution of FCFDE is obtained. The related theorems and properties are proved in detail and the method is illustrated by solving some examples.

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Please cite this article as: Z. Gouyandeh, T. Allahviranloo, A. Armand, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via Tau-collocation method with convergence analysis, Journal of Computational and Applied Mathematics (2016), http://dx. AbstractIn this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear Volterra-Fredholm-Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra-Fredholm-Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L 2 -norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra-Fredholm-Hammerstein integral equations.