Analytical solutions of linear and non-linear incommensurate fractional-order coupled systems

In this paper, a new analytical method is developed for solving linear and non-linear fractional-order coupled systems of incommensurate orders. The system consists of two fractional-order differential equations of orders 0< α, β ≤1. The proposed approach is performed by decoupling the system into two fractional-order differential equations; the first one is a fractional-order differential equation (FoDE) of one variable of order (α+β), while the second one depends on the solution of the first one. The general solution of the coupled system is obtained using the adomian decomposition method (ADM). The main ideas of this work are verified via several examples of linear and nonlinear systems, and the numerical simulations are performed using mathematica.