Abstract
A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO-FPEs) is considered. We propose a shifted Legendre-Gauss-Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev-Gauss-Radau collocation (SC-GR-C) method to solve the two-dimensional VO-FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO-FPEs is revealed, even when dealing with non-smooth time solutions.