Numerical study of the variable-order fractional version of the nonlinear fourth-order 2D diffusion-wave equation via 2D Chebyshev wavelets

In this article, the 2D Chebyshev wavelets (CWs) are used for designing a proper procedure to solve the variable-order (VO) fractional version of the nonlinear fourth-order diffusion-wave (DW) equation. In the presented model, fractional derivatives are defined in the Caputo type. The $$\theta $$-weighted finite difference technique is utilized to approximate the VO time fractional derivative through a recursive algorithm. By expanding the unknown solution in terms of the 2D CWs and substituting in the recursive equation, a linear system of algebraic equation is obtained. The accuracy of the method is studied on some numerical example.