A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations

In this paper, the pseudo-spectral method is generalized for solving fractional differential equations with initial conditions. For this purpose, an appropriate representation of the solution is presented and the pseudo-spectral differentiation matrix of fractional order is derived. Then, by using pseudo-spectral scheme, the problem is reduced to the solution of a system of algebraic equations. Through several numerical examples, we evaluate the accuracy and performance of our proposed method.

Research highlights
► We consider the numerical solution of three-term fractional differential equations.
► We approximate the unknown solution with a finite sum with unknown coefficients.
► We introduce a method for driving the Pseudo-spectral fractional derivative matrix.
► The problem is reduced to a linear algebraic equation which can be easily solved.
► The method is applied on some examples and the results are reported and compared.