{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:21Z","timestamp":1760240781671,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T00:00:00Z","timestamp":1569283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper presents new results in implementation of parallel computing in modeling of fractional-order state-space systems. The methods considered in the paper are based on the Euler fixed-step discretization scheme and the Gr\u00fcnwald-Letnikov definition of the fractional-order derivative. Two different parallelization approaches for modeling of fractional-order state-space systems are proposed, which are implemented both in Central Processing Unit (CPU)- and Graphical Processing Unit (GPU)-based hardware environments. Simulation examples show high efficiency of the introduced parallelization schemes. Execution times of the introduced methodology are significantly lower than for the classical, commonly used simulation environment.<\/jats:p>","DOI":"10.3390\/e21100931","type":"journal-article","created":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T03:51:18Z","timestamp":1569383478000},"page":"931","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Parallel Implementation of Modeling of Fractional-Order State-Space Systems Using the Fixed-Step Euler Method"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6014-3682","authenticated-orcid":false,"given":"Rafa\u0142","family":"Stanis\u0142awski","sequence":"first","affiliation":[{"name":"Departament of Electrial, Control and Computer Engineering, Opole University of Technology, 45-758 Opole, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0475-6556","authenticated-orcid":false,"given":"Kamil","family":"Kozio\u0142","sequence":"additional","affiliation":[{"name":"Departament of Electrial, Control and Computer Engineering, Opole University of Technology, 45-758 Opole, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bauer, W., and Rydel, M. 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