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Finally, several numerically simulations are carried out to illustrate the broad applicability of our theoretical findings.<\/jats:p>","DOI":"10.1007\/s40314-023-02274-1","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T06:47:42Z","timestamp":1680504462000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Constructing reliable approximations of the random fractional Hermite equation: solution, moments and density"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6385-4263","authenticated-orcid":false,"given":"Clara","family":"Burgos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom\u00e1s","family":"Caraballo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Carlos","family":"Cort\u00e9s","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laura","family":"Villafuerte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafael Jacinto","family":"Villanueva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,4,1]]},"reference":[{"key":"2274_CR1","doi-asserted-by":"publisher","unstructured":"AbdelAty AM, Soltan A, Ahmed W, Radwan AG (2016) Hermite polynomials in the fractional order domain suitable for special filters design. 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