Generalization of generalized orthogonal polynomial operational matrices for fractional and operational calculus

Abstract

A method is given for the approximation of generalized orthogonal polynomials (GOP) to solve the problems of fractional and operational calculus. A more rigorous derivation for the generalized orthogonal polynomial operational matrices is proposed. The Riemann-Liouville fractional integral for repeated fractional (and operational) integration is integrated exactly, then expanded in generalized orthogonal polynomials to yield the generalized orthogonal polynomial operational matrices. The generalized orthogonal polynomial operational matrices perform as s^α(α ≥ αε R) in the Laplace domain and as fractional (and operational) integrators in the time domain. Using these results, inversions of the Laplace transforms of irrational and rational transfer functions are solved in a simple way. Very accurate results are obtained.