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In this paper, we derived a new operational matrix of fractional integration of arbitrary order for modified generalized Laguerre polynomials. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with the modified generalized Laguerre tau method for solving general linear multi-term fractional differential equations (FDEs). Only small dimension of a modified generalized Laguerre operational matrix is needed to obtain a satisfactorydoi:10.1186/1687-1847-2012-179 fatcat:3xgfqot3jfahjgrromot6fgzw4