Modified Laguerre operational matrices for fractional calculus and applications

Abstract

The modified Laguerre polynomial is defined with an additional parameter from the conventional one and is applied to approach the problems of fractional calculus. First, the operational matrices for the integration and the differentiation of the modified Laguerre polynomials are derived. The generalized operational matrices corresponding to s, 1/s, s/(s2 + 1) 1/2 exp [ − s/(s + 1)] are derived as examples. Comparison of the modified Laguerre series approximate inversions of irrational Laplace transforms with exact solution shows that the present modification method is much better than the conventional one. In addition, the present proposed modified Laguerre polynomials can also be used to approximate the solution of fractional calculus which cannot be obtained from conventional Laguerre polynomials.