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Abstract The exact solution of fractional combined Korteweg-de Vries and modified Korteweg-de Vries (KdV–mKdV) equation is obtained by using the (1/G′) $(1/G^{\prime})$ expansion method. To investigate a geometrical surface of the exact solution, we choose γ=1 $\gamma=1$. The collocation method is applied to the fractional combined KdV–mKdV equation with the help of radial basis for 0<γ<1 $0<\gamma<1$. L2 $L_{2}$ and L∞ $L_{\infty}$ 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.