{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T11:30:03Z","timestamp":1774438203955,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,11]],"date-time":"2018-01-11T00:00:00Z","timestamp":1515628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time derivatives       C ^   N F    (   k \u2192  , t  )      and then introduce time fractional derivatives in their equations of motion and calculate the corresponding fractional correlation function. We find that the magnitude of the fractional correlation       C ^  F   (   k \u2192  , t  )      is always lower than the non-fractional one and decays more rapidly. The relationship between the fractional loss modulus      G F \u2033   ( \u03c9 )      and       C ^  F   (   k \u2192  , t  )      is also calculated analytically. The difference between the values of      G \u2033   ( \u03c9 )      for two specific viscoelastic fluids is quantified. Our model calculation shows that the fractional effects on this measurable quantity may be three times as large as compared with its non-fractional value. The fact that the dynamic shear modulus is related to the light scattering spectrum suggests that the measurement of this property might be used as a suitable test to assess the effects of temporal fractional derivatives on a measurable property. Finally, we summarize the main results of our approach and emphasize that the eventual validity of our model calculations can only come from experimentation.<\/jats:p>","DOI":"10.3390\/e20010028","type":"journal-article","created":{"date-parts":[[2018,1,11]],"date-time":"2018-01-11T13:36:15Z","timestamp":1515677775000},"page":"28","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Fractional Time Fluctuations in Viscoelasticity: A Comparative Study of Correlations and Elastic Moduli"],"prefix":"10.3390","volume":"20","author":[{"given":"Rosal\u00edo","family":"Rodr\u00edguez","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, Cd. de M\u00e9xico 01000, Mexico"},{"name":"Sistema Nacional de Investigadores, Mexico City 03940, Mexico"},{"name":"Proyecto Universitario de Fen\u00f3menos Lineales y Mec\u00e1nica (FENOMEC), Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, Cd. de M\u00e9xico 01000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elizabeth","family":"Salinas-Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Sistema Nacional de Investigadores, Mexico City 03940, Mexico"},{"name":"Departamento I. P. H., Universidad Aut\u00f3noma Metropolitana, Iztapalapa, Apdo. Postal 55-534, Cd. de M\u00e9xico 09340, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge","family":"Fujioka","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, Cd. de M\u00e9xico 01000, Mexico"},{"name":"Sistema Nacional de Investigadores, Mexico City 03940, Mexico"},{"name":"Proyecto Universitario de Fen\u00f3menos Lineales y Mec\u00e1nica (FENOMEC), Universidad Nacional Aut\u00f3noma de M\u00e9xico, Apdo. Postal 20-364, Cd. de M\u00e9xico 01000, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1146\/annurev.pc.16.100165.000435","article-title":"Time-correlation functions and transport coefficients in statistical mechanics","volume":"16","author":"Zwanzig","year":"1964","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1103\/PhysRev.91.1505","article-title":"Fluctuations and Irreversible Processes","volume":"91","author":"Onsager","year":"1953","journal-title":"Phys. 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