A Pseudo-Spectral Method for Solving Fractional Differential Equations

Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. 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.

Keywords:

Caputo derivative , Fractional differential equations , Fractional differentiation matrix