Piecewise Polynomial Least Squares Method for Differential Equations of Fractional Order

In this paper a new method to compute approximate analytical solutions for differential equations of fractional order is presented. The proposed computational method, called the Piecewise Polynomial Least Squares Method (PWPLSM), is a combination of the Polynomial Least Squares Method and of piecewise-defined functions. Numerical results for differential equations of different fractional orders are discussed. The approximate solutions obtained with PWPLSM are compared with other existing analytical and numerical solutions. The tables and figures included demonstrate the accuracy of the new method.