**6. Conclusions**

In this paper, a system of fractional\_order differential equations was examined by drawing from a new operational matrix of the fractional derivative in some special conditions. We also systematized a very operational algorithm in order to attain the solution of the linear and nonlinear systems of fractional differential equations in Maple. All numerical results and graphical presentations generated by Maple affirmed that the Legendre wavelet operational matrix method is very effective and applicable. As the next step, the method introduced in this paper can be applied to fractional partial differential equations and the system of such equations, fractional integral equations and the system of such equations, and fractional integro-differential equations. These equations are at least as important as fractional differential equations and they are very significant in science, engineering, and technology.

**Author Contributions:** All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
