<p>A novel investigation on numerical methods for solving the variable order nonlinear space-time fractional KdV-Burgers-Kuramoto equation is presented in this paper. These techniques employ orthonormal Euler wavelets (OEWs) and Jacobi wavelets (JWs) efficiently to obtain accurate numerical solutions for the considered model equation. Using these wavelets, the integral operational matrices and the operational matrices for the variable-order space-time fractional derivative were devised to implement the proposed numerical techniques. These matrices are exerted into the variable-order nonlinear space-time fractional KdV-Burgers-Kuramoto equation, and utilizing suitable collocation points, the original equation is transformed into a system of algebraic equations. Finally, by numerically solving the resulting equations, we acquire the solution to the problem that is being considered. Additionally, several pertinent theorems are examined conscientiously to assess the convergence analysis and error estimate of the proposed numerical approach based on the two-dimensional wavelets technique. Some numerical examples are presented to demonstrate the computational efficiency and applicability of the proposed numerical method.</p>