Numerical solutions of fractional differential equations by using fractional Taylor basis

In this paper, a new numerical method for solving fractional differential equations U+0028 FDEs U+0029 is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.