A shifted Gegenbauer spectral method for the multi-term time-fractional partial differential equations

In this paper, we propose an efficient operational formulation of spectral tau method for multi-term time fractional differential equations (FDEs) with initial-boundary conditions. The shifted Gegenbauer polynomials operational matrices of RiemannLiouville fractional integral and Caputo fractional derivatives are presented. By using these operational matrices, we propose the shifted Gegenbauer polynomials tau method for both temporal and spatial discretization, which allows us to present an efficient spectral method for solving such problem. Finally, numerical results show good agreement with the theoretical analysis.