In this study, numerical solutions of the fractional Harry Dym equation are investigated. Linearization techniques are utilized for non-linear terms existing in the fractional Harry Dym equation. The error norms L2 and L∞ are computed. Stability of the finite difference method is studied with the aid of Von Neumann stabity analysis.

The exact solution of fractional combined Korteweg-de Vries and modified Korteweg-de Vries (KdV-mKdV) equation is obtained by using the (1/G ) expansion method. To investigate a geometrical surface of the exact solution, we choose γ = 1.The collocation method is applied to the fractional combined KdV-mKdV equation with the help of radial basis for 0 < γ < 1. L 2 and L ∞ error norms are computed with the Mathematica program. Stability is investigated by the Von-Neumann analysis. Instable numerical solutions are obtained as the number of node points increases. It is shown that the reason for this situation is that the exact solution contains some degenerate points in the Lorentz-Minkowski space.

Non-linear terms of the time-fractional KdV-Burgers-Kuramoto equation are linearized using by some linearization techniques. Numerical solutions of this equation are obtained with the help of the finite difference methods. Numerical solutions and corresponding analytical solutions are compared. The L2 and L? error norms are computed. Stability of given method is investigated by using the Von Neumann stability analysis.

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