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Abstract
The Laguerre operational matrices for the integration and differentiation of a Laguerre vector whose elements are Laguerre polynomials are generalized to fractional calculus for investigating distributed systems. The generalized operational matrices corresponding to 8, 1/8, 8/√(82+1) and exp (−8/(8+1)) are derived as examples. Comparison of the Laguerre series approximate inversions of irrational Laplace transforms with exact solutions is very satisfactory.