{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:04:22Z","timestamp":1777377862771,"version":"3.51.4"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T00:00:00Z","timestamp":1632268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/MAT\/04674\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/04674\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007684","name":"Ministry of Education and Science of Ukraine","doi-asserted-by":"publisher","award":["0119U002583"],"award-info":[{"award-number":["0119U002583"]}],"id":[{"id":"10.13039\/501100007684","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the asymptotic behavior of the random time dynamical systems. It turns out that for the special case of stable subordinators explicit expressions for the subordination are known and its asymptotic behavior are derived. For more general classes of random time changes explicit calculations are essentially more complicated and we reduce our study to the asymptotic behavior of the corresponding Cesaro limit.<\/jats:p>","DOI":"10.3390\/fractalfract5040133","type":"journal-article","created":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T22:50:48Z","timestamp":1632351048000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Cesaro Limits for Fractional Dynamics"],"prefix":"10.3390","volume":"5","author":[{"given":"Yuri","family":"Kondratiev","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Bielefeld, D-33615 Bielefeld, Germany"},{"name":"Institute of Mathematics of the National Academy of Sciences of Ukraine, National Pedagogical Dragomanov University, 33615 Kiev, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5207-1703","authenticated-orcid":false,"given":"Jos\u00e9","family":"da Silva","sequence":"additional","affiliation":[{"name":"CIMA, University of Madeira, Campus da Penteada, 9020-105 Funchal, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,22]]},"reference":[{"key":"ref_1","unstructured":"Kondratiev, Y., and da Silva, J. 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Regular Variation; Encyclopedia of Mathematics and its Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511721434"}],"container-title":["Fractal and Fractional"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-3110\/5\/4\/133\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:03:05Z","timestamp":1760166185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-3110\/5\/4\/133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,22]]},"references-count":18,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["fractalfract5040133"],"URL":"https:\/\/doi.org\/10.3390\/fractalfract5040133","relation":{},"ISSN":["2504-3110"],"issn-type":[{"value":"2504-3110","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,22]]}}}