On the Generalization of Block Pulse Operational Matrices for Fractional and Operational Calculus

Chi-Hsu Wang*

*Corresponding author for this work

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

A more rigorous derivation for the generalized block pulse operational matrices is proposed in this paper. The Riemann-Liouville fractional integral for repeated fractional (and operational) integration is integrated exactly, then expanded in block pulse functions to yield the generalized block pulse operational matrices. The generalized block pulse operational matrices perform as s(α\s>;0,α∈R) in the Laplace domain and as fractional (and operational) integrators in the time domain. Also, the generalized block pulse operational matrices of differentiation which correspond to sα(α\s>;0,α∈R) in the Laplace domain are derived. Based on these results, the inversions of rational and irrational transfer functions are proposed in a simple, accurate and efficient way.

Original languageEnglish
Pages (from-to)91-102
Number of pages12
JournalJournal of the Franklin Institute
Volume315
Issue number2
DOIs
StatePublished - 1 Jan 1983

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