Time-space spectral Galerkin method for time-fractional fourth-order partial differential equations

The goal of this paper is to present a high-order numerical scheme for solving fourth-order time-fractional partial differential equations (TFPDEs). The fractional derivative in the considered model is in Caputo’s sense. In the proposed approach, the time variable is approximated by the Legendre polynomials, and space discretisation is based on the modified basis constructed from a combination of the Legendre polynomials. We study the stability and convergence of the proposed method. Some numerical examples are investigated to validate the efficiency, accuracy, and theoretical results of the given method.