A New Optimized Method for Solving Variable-Order Fractional Differential Equations

In this paper, a new optimized method based on polynomi-als is proposed for solving variable-order fractional differential equations (V-FDEs) and systems of V-FDEs. To do this, a general polynomial of degree m with unknown coefficients is considered as an approximate solution for the problem under study. By using the initial conditions some of these unknown coefficients are obtained. Finally the rest of these unknown coefficients are obtained optimally by minimizing error of 2-norm of the approximate solution in a desired interval. In order to demonstrate the accuracy and efficiency of the proposed method some numerical examples are given.