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Corresponding Matlab\u00a9\u00a0 codes have been also made available on the internet, proving to be very competitive w.r.t. existing ones. However, so far, FHBVMs have been given for solving systems of fractional differential equations with the same order of fractional derivative, whereas the numerical solution of multi-order problems (i.e., problems in which different orders of fractional derivatives occur) has not been handled, yet. Due to their relevance in applications, in this paper we propose an extension of FHBVMs for addressing fractional multi-order problems, providing full details for such an approach. A corresponding Matlab\u00a9\u00a0code, handling the case of two different fractional orders, is also made available, proving very effective for numerically solving these problems.<\/jats:p>","DOI":"10.1007\/s10915-026-03315-7","type":"journal-article","created":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T01:27:36Z","timestamp":1778290056000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Multi-Order Extension of Fractional HBVMs (FHBVMs)"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6290-4107","authenticated-orcid":false,"given":"Luigi","family":"Brugnano","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianmarco","family":"Gurioli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felice","family":"Iavernaro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikk","family":"Vikerpuur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,9]]},"reference":[{"key":"3315_CR1","doi-asserted-by":"publisher","first-page":"4862650","DOI":"10.1155\/2022\/4862650","volume":"2022","author":"AI Ahmed","year":"2022","unstructured":"Ahmed, A.I., Al-Ahmary, T.A.: Fractional-order Chelyshkov collocation method for solving systems of fractional differential equations. 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