A pseudo‐operational collocation method for variable‐order time‐space fractional KdV–Burgers–Kuramoto equation

Abstract

The idea of this work is to provide a pseudo‐operational collocation scheme to deal with the solution of the variable‐order time‐space fractional KdV–Burgers–Kuramoto equation (VOSTFKBKE). Such the fractional partial differential equation (FPDE) has three characteristics of dissipation, dispersion, and instability, which make this equation is used to model many phenomena in diverse fields of physics. Numerical solutions are sought in a linear combination of two‐dimensional Jacobi polynomials as basis functions. In order to approximate unknown functions in terms of the basis vector, pseudo‐operational matrices are constructed to avoid integration. An error bound of the residual function is estimated in a Jacobi‐weighted space in the norms. Numerical results are compared with exact ones and those reported by other researchers to demonstrate the effectiveness of the recommended method.