- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

In this paper, we propose a new numerical algorithm for the approximate solution of non-homogeneous fractional differential equation. Using this algorithm the fractional differential equations are transformed into a system of algebraic linear equations by operational matrices of block-pulse and hybrid functions. Based on our new algorithm, this system of algebraic linear equations can be solved by a proposed (TSI) method. Further, some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm.

fractional differential equation, Block-pulse wavelet, Hybrid function, Operational matrices, Two stage iterative method