A numerical scheme for solving differential equations with space and time-fractional coordinate derivatives

Abstract

In this paper, we apply a numerical scheme for solving fractional differential equations. Our approach is based on an operational matrix of fractional Riemann-Liouville integration with Legendre basis and zeros of Chebyshev polynomials. In this framework the fractional Burgers equation, modified fractional Korteweg-de Vries equation and fractional wave equation are considered as prototype examples. The results reveal that the present method is very effective and accurate.

Keywords: Chebyshev polynomials, fractional differential equations,  Legendre basis, operational matrix.