This paper introduces a new numerical mechanism for solving multi- order fractional dierential equations (MOFDEs)
and systems of fractional dierential equations, in which the fractional derivatives are expressed in Riemman- liouville
(RL) sense. A new shifted ultraspherical (Gegenbauer) operational matrix (SGOM) of fractional integration of arbitrary
order is induced. By using this matrix jointly with the Tau method, the solution of fractional dierential equation (FDE)
is decreased to the solution of a system of algebraic equations (AEs). Helpful problems are built-in to show the powerful
and validity of the proposed technique.