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In this paper we propose the collocation method to achieve the numerical solution of fractional order linear
systems where a Fractional Derivative is defined in the Caputo sense.We use Taylor collocation method,
which is based on collocation method for solving fractional differential equation. This method is based on
first taking the truncated Taylor expansions of the vector function’s solution in the Fractional order linear
system and then substituting their matrix forms into the system. Using collocation points, we have a system
of linear algebraic equation.The method has been tested by some numerical examples.