{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:43:41Z","timestamp":1760237021170,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, local fractional cylindrical wave solutions on Signorini hyperelastic materials are studied. In particular, we focus on the so-called Signorini potential. Cantor-type cylindrical coordinates are used to analyze, both from dynamical and geometrical point of view, wave solutions, so that the nonlinear fundamental equations of the fractional model are explicitly given. In the special case of linear approximation we explicitly compute the fractional wave profile.<\/jats:p>","DOI":"10.3390\/axioms9010022","type":"journal-article","created":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T10:09:57Z","timestamp":1581674997000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Cantor Waves for Signorini Hyperelastic Materials with Cylindrical Symmetry"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"first","affiliation":[{"name":"Engineering School (DEIM), Tuscia University, 01100 Viterbo, Italy"},{"name":"Azerbaijan University, Baku AZ1007, Azerbaijan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,13]]},"reference":[{"unstructured":"Achenbach, J.D. (1973). Wave Propagation in Solids, North-Holland.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Cattani, C., and Rushchitsky, J.J. (2007). Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, World Scientific.","key":"ref_2","DOI":"10.1142\/9789812709769"},{"unstructured":"Ogden, R.W. (1974). Non-Linear Elastic Deformations, Dover.","key":"ref_3"},{"doi-asserted-by":"crossref","unstructured":"Bower, A. (2009). Applied Mechanics of Solids, CRC Press.","key":"ref_4","DOI":"10.1201\/9781439802489"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF02418157","article-title":"Trasformazioni termoelastiche finite","volume":"22","author":"Signorini","year":"1943","journal-title":"Ann. Mater. 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Handbook of Differential Equations, Academic Press. [3rd ed.].","key":"ref_12"},{"unstructured":"Yang, X.J. (2012). Advanced Local Fractional Calculus and Its Applications, World Science.","key":"ref_13"},{"unstructured":"Pobludny, I. (1999). Fractional Differential Equations, Academic Press.","key":"ref_14"},{"doi-asserted-by":"crossref","unstructured":"Ortigueira, M.D. (2011). Fractional Calculus for Scientists and Engineers, Springer.","key":"ref_15","DOI":"10.1007\/978-94-007-0747-4"},{"doi-asserted-by":"crossref","unstructured":"Herrmann, R. (2014). Fractional Calculus, World Scientific. [2nd ed.].","key":"ref_16","DOI":"10.1142\/8934"},{"doi-asserted-by":"crossref","unstructured":"Cattani, C., Srivastava, H.M., and Yang, X.-J. (2015). Fractional Dynamics, Walter de Gruyter GmbH & Co KG.","key":"ref_17","DOI":"10.1515\/9783110472097"},{"doi-asserted-by":"crossref","unstructured":"Yang, X.J., Baleanu, D., and Srivastava, H.M. (2016). 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