{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T03:55:02Z","timestamp":1773287702567,"version":"3.50.1"},"reference-count":14,"publisher":"SAGE Publications","issue":"9-10","license":[{"start":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T00:00:00Z","timestamp":1220227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:p> Fractional calculus (FC) is no longer considered solely from a mathematical viewpoint, and is now applied in many emerging scientific areas, such as electricity, magnetism, mechanics, fluid dynamics, and medicine. In the field of dynamical systems, significant work has been carried out proving the importance of fractional order mathematical models. This article studies the electrical impedance of vegetables and fruits from a FC perspective. From this line of thought, several experiments are developed for measuring the impedance of botanical elements. The results are analyzed using Bode and polar diagrams, which lead to electrical circuit models revealing fractional-order behaviour. <\/jats:p>","DOI":"10.1177\/1077546307087442","type":"journal-article","created":{"date-parts":[[2008,9,30]],"date-time":"2008-09-30T13:57:52Z","timestamp":1222783072000},"page":"1389-1402","source":"Crossref","is-referenced-by-count":128,"title":["Fractional Electrical Impedances in Botanical Elements"],"prefix":"10.1177","volume":"14","author":[{"given":"Isabel S.","family":"Jesus","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 4200-072 Porto, Portugal,"}]},{"given":"J.A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 4200-072 Porto, Portugal"}]},{"given":"J.","family":"Boaventure Cunha","sequence":"additional","affiliation":[{"name":"Engineering Department, University of Tr\u00e1s-os-Montes and Alto Douro, Vila-Real, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2008,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/0471716243"},{"key":"atypb2","volume-title":"Analog realization of a fractional order control element","author":"Bohannan, G.W.","year":"2002"},{"key":"atypb3","volume-title":"Electromagnetic Theory","author":"Heaviside, O.","year":"1893"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1149\/1.2129668"},{"key":"atypb5","volume-title":"Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications","author":"Jesus, I.S."},{"key":"atypb6","volume-title":"Proceedings of the 25th IASTED International Conference on Modeling, Identification and Control","author":"Jesus, I.S."},{"key":"atypb7","volume-title":"Dielectric Relaxation in Solids","author":"Jonscher, A.K.","year":"1993"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2738(02)00222-9"},{"key":"atypb9","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller, K.S.","year":"2002"},{"key":"atypb10","volume-title":"The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order","author":"Oldham, K.B.","year":"1974"},{"key":"atypb11","volume-title":"La D\u00e9rivation Non Entier: Th\u00e9orie, Synth\u00e8se et Applications","author":"Oustaloup, A.","year":"1995"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/4.735545"},{"key":"atypb13","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"Samko S.G.","year":"1993"},{"issue":"4","key":"atypb14","first-page":"403","volume":"7","author":"Tenreiro Machado, J.A.","year":"2004","journal-title":"Journal of Fractional Calculus & Applied Analysis"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087442","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087442","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T09:19:36Z","timestamp":1740993576000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546307087442"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":14,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["10.1177\/1077546307087442"],"URL":"https:\/\/doi.org\/10.1177\/1077546307087442","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"value":"1077-5463","type":"print"},{"value":"1741-2986","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}