Properties of solutions for fractional-order linear system with differential equations

In this paper, we study the analytical solutions of two-dimensional fractional-order linear system ${\mathcal{D}}_t^{\alpha }X(t)=AX(t)$ described by fractional differential equations, where $\mathcal{D}$ is the fractional derivative in the Caputo-Fabrizio sense and $A=(a_{ij}{)}_{2\times 2}$ is nonsingular coefficient matrix with $a_{ij}\in \mathbb{R}$. The analytical solutions of fractional-order linear system will be compared to the solution of classical linear system. Examples are provided to characterize the behavior of the solutions for fractional-order linear system.