**Authors: **Salisu Ibrahim^{1 } & Abdulnasir Isah^{2 }

^{1}Department of Mathematics Education, Faculty of education. Tishk International University, Erbil, Iraq

^{2}Department of Mathematics Education, Faculty of education. Tishk International University, Erbil, Iraq

**Abstract:** This paper presents approximate solutions of linear system of fractional differential equations (FDEs) by extending the approach of shifted Legendre operational matrix of derivatives together with spectral method. The results obtained in solving differential systems of linear FDE shows that the proposed method is factual. Fractional differential equations (FDEs) have been a useful tool for computing and modelling of computer components in telecommunication companies, mobile companies and for industrial practitioners and also plays a vital role in science and engineering.

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