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We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives leaving their order as a free parameter. All this with the intention to explain the current observed acceleration of the Universe. We apply the Last Step Modification technique of fractional calculus to construct some useful fractional equations of cosmology. The fits of the unknown fractional derivative order and the fractional cosmographic parameters to SN Ia data shows that this simple construction can explain the current accelerated expansion of the Universe without the use of a dark energy component with a MOND-like behaviour using Milgrom\u2019s acceleration constant which sheds light into to the non-necessity of a dark matter component as well.<\/jats:p>","DOI":"10.3390\/sym13020174","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"174","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Extending Friedmann Equations Using Fractional Derivatives Using a Last Step Modification Technique: The Case of a Matter Dominated Accelerated Expanding Universe"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5355-9674","authenticated-orcid":false,"given":"Ernesto","family":"Barrientos","sequence":"first","affiliation":[{"name":"Instituto de Astronom\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, AP 70-264, Ciudad de M\u00e9xico 04510, Mexico"},{"name":"Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Departamento de Matem\u00e1ticas y Mec\u00e1nica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2143-5973","authenticated-orcid":false,"given":"Sergio","family":"Mendoza","sequence":"additional","affiliation":[{"name":"Instituto de Astronom\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico, AP 70-264, Ciudad de M\u00e9xico 04510, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pablo","family":"Padilla","sequence":"additional","affiliation":[{"name":"Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Departamento de Matem\u00e1ticas y Mec\u00e1nica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad de M\u00e9xico 04510, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Will, C.M. 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