{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T03:45:43Z","timestamp":1779248743636,"version":"3.51.4"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p>Memristor, the missing fourth passive circuit element predicted forty years ago by Chua was recognized as a nanoscale device in 2008 by researchers of a H. P. Laboratory. Recently the notion of memristive systems was extended to capacitive and inductive elements, namely, memcapacitor and meminductor whose properties depend on the state and history of the system. In this paper, we use fractional calculus to generalize and provide a mathematical paradigm for describing the behavior of such elements with memory. In this framework, we extend Ohm's law to the generalized Ohm's law and prove it.<\/jats:p>","DOI":"10.1142\/s0218127414300237","type":"journal-article","created":{"date-parts":[[2014,10,3]],"date-time":"2014-10-03T08:25:41Z","timestamp":1412324741000},"page":"1430023","source":"Crossref","is-referenced-by-count":118,"title":["Memfractance: A Mathematical Paradigm for Circuit Elements with Memory"],"prefix":"10.1142","volume":"24","author":[{"given":"Mohammed-Salah","family":"Abdelouahab","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University Center of Mila, Mila 43000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ren\u00e9","family":"Lozi","sequence":"additional","affiliation":[{"name":"Laboratory of Mathematics J. A. Dieudonn\u00e9, U.M.R. CNRS 7351, University of Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leon","family":"Chua","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,10,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2514\/3.20641"},{"key":"rf2","unstructured":"G.\u00a0Bohannan, Analog Realization of a Fractional Control Element \u2014 Revisited (2002)\u00a0pp. 175\u2013182."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/9789812817747_0001"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-246X.1967.tb02303.x"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083337"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1976.10092"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2003.818319"},{"key":"rf8","volume-title":"Introduction to Memristors","author":"Chua L. 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