{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T05:00:49Z","timestamp":1772341249061,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T00:00:00Z","timestamp":1748304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES)","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES)","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES)","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]},{"name":"Universidade Federal de Juiz de Fora (UFJF)","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"Universidade Federal de Juiz de Fora (UFJF)","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"Universidade Federal de Juiz de Fora (UFJF)","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]},{"name":"Universidade da Beira Interior (UBI)","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"Universidade da Beira Interior (UBI)","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"Universidade da Beira Interior (UBI)","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]},{"name":"CMA-UBI plus the COST Actions CA23130","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"CMA-UBI plus the COST Actions CA23130","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"CMA-UBI plus the COST Actions CA23130","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]},{"name":"Relativistic Quantum Information (RQI)","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"Relativistic Quantum Information (RQI)","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"Relativistic Quantum Information (RQI)","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]},{"name":"FAPEMIG","award":["UID-B-MAT\/00212\/2020"],"award-info":[{"award-number":["UID-B-MAT\/00212\/2020"]}]},{"name":"FAPEMIG","award":["CA23115"],"award-info":[{"award-number":["CA23115"]}]},{"name":"FAPEMIG","award":["APQ-06640-24"],"award-info":[{"award-number":["APQ-06640-24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant (\u039b), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter \u03b1, where 1&lt;\u03b1\u22642, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of \u03b1, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value \u03b1=2 (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for \u039b (in a non-fractional conventional set-up) versus balancing, e.g., both \u039b and \u03b1 in the fractional framework.<\/jats:p>","DOI":"10.3390\/fractalfract9060349","type":"journal-article","created":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T09:29:36Z","timestamp":1748338176000},"page":"349","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0820-5700","authenticated-orcid":false,"given":"Daniel L.","family":"Canedo","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Instituto de Ci\u00eancias Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-330, MG, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7170-8952","authenticated-orcid":false,"given":"Paulo","family":"Moniz","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es (CMA-UBI), Universidade da Beira Interior, Rua Marqu\u00eas d\u2019\u00c1vila e Bolama, 6200 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7111-9151","authenticated-orcid":false,"given":"Gil","family":"Oliveira-Neto","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Instituto de Ci\u00eancias Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-330, MG, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1103\/PhysRev.160.1113","article-title":"Quantum Theory of Gravity. 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