Generalization of generalized orthogonal polynomial operational matrices for fractional and operational calculus
作者:
MAW-LING WANG,
RONG-YEU CHANG,
SHWU-YIEN YANG,
期刊:
International Journal of Systems Science
(Taylor Available online 1987)
卷期:
Volume 18,
issue 5
页码: 931-943
ISSN:0020-7721
年代: 1987
DOI:10.1080/00207728708964020
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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 sα(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.
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