{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:05:40Z","timestamp":1760144740691,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,4]],"date-time":"2024-05-04T00:00:00Z","timestamp":1714780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Differentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators. Fractional differentiation of Jacobi orthogonal polynomials can be expressed explicitly through Jacobi\u2013Jacobi transformations between two indexes. In the current paper, an algorithm is presented to construct a fractional differentiation matrix with a matrix representation for Riemann\u2013Liouville, Caputo and Riesz derivatives, which makes the computation stable and efficient. Applications of the fractional differentiation matrix with the spectral collocation method to various problems, including fractional eigenvalue problems and fractional ordinary and partial differential equations, are presented to show the effectiveness of the presented method.<\/jats:p>","DOI":"10.3390\/axioms13050305","type":"journal-article","created":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T14:26:11Z","timestamp":1715005571000},"page":"305","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Construction of Fractional Pseudospectral Differentiation Matrices with Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Wenbin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China"}]},{"given":"Hongjun","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9759-7434","authenticated-orcid":false,"given":"Tinggang","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0168-9274(99)00078-1","article-title":"On the computation of high order pseudospectral derivatives","volume":"33","author":"Costa","year":"2000","journal-title":"Appl. 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