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Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.<\/jats:p>","DOI":"10.3390\/e24020143","type":"journal-article","created":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T08:09:20Z","timestamp":1642493360000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Exact and Numerical Solution of the Fractional Sturm\u2013Liouville Problem with Neumann Boundary Conditions"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1029-1863","authenticated-orcid":false,"given":"Malgorzata","family":"Klimek","sequence":"first","affiliation":[{"name":"Department of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-200 Czestochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3695-9569","authenticated-orcid":false,"given":"Mariusz","family":"Ciesielski","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Czestochowa University of Technology, Dabrowskiego 73, 42-200 Czestochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2818-402X","authenticated-orcid":false,"given":"Tomasz","family":"Blaszczyk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-200 Czestochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zettl, A. (2010). Sturm\u2013Liouville Theory, American Mathematical Society. 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