In this paper, the variational iteration method is used for solving the generalized KdV–Burgers' (GKdVB(p,m,q)) equations with nonzero parameters p, m and q. We can see the GKdVB (p, m,q) equations from another point of view as the generalized Burgers' (GB(p, m, q)) equations and the generalized KdV (GKdV(p, m, q)) equations by considering various parameters. Two test problems are used to demonstrate the accuracy of our technique.
The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) on the half line with constant coefficients using a generalized Laguerre tau (GLT) method. The fractional derivatives are described in the Caputo sense. We state and prove a new formula expressing explicitly the derivatives of generalized Laguerre polynomials of any degree and for any fractional order in terms of generalized Laguerre polynomials themselves. We develop also a direct solution technique for solving the linear multi-order FDEs with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives described in the Caputo sense are based on generalized Laguerre polynomials [Formula: see text] with [Formula: see text] and i denoting the polynomial degree.
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