ON SYSTEMS OF FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS FOR ORDER 1 < 𝜗 ≤ 2

Abstract

This work is devoted to establish a numerical scheme for system of fractional-order differential equations (FODEs) with order [Formula: see text]. The scheme is established by using Bernstein polynomials (BPs). Based on the said materials, some operational matrices are formed. With the help of obtained operational matrices, the considered system is reduced to some algebraic system of equations. On using MATLAB-16, the system is then solved to get the required numerical solution for the proposed system. Several examples are treated with the help of the proposed method for numerical solutions. Further, error analysis is also recorded for different fractional orders and various scale levels. The mentioned results are displayed graphically. Comparison with exact solution at traditional order derivative is also given. It should be kept in mind that the proposed method does not require any kind of discretization or collocation. Also, there is no external parameter which controls the method. Due to these features, the proposed method is powerful and efficient for different classes of FODEs to compute their numerical solutions. The efficiency of the proposed method can be enhanced by increasing the scale level.