DE Sinc-Legendre collocation method for time fractional partial differential equations

In this paper, a new version of Sinc-Legendre collocation method based on Double Exponential (DE) transformation is implemented for a class of space-time fractional convection-diffusion equations on a bounded domain that involve temporal Caputo derivative of order α ∈ (0, 1]. The approach is based on the collocation technique where the shifted Legendre polynomials in time and the DE Sinc functions in space are employed, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Numerical examples are included to demonstrate the validity and significant advantages of the technique and a comparison is made with existing results in the latest literature