{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:38:17Z","timestamp":1753879097262,"version":"3.41.2"},"reference-count":12,"publisher":"ASME International","issue":"3","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2011,7,1]]},"abstract":"<jats:p>The generalized Gr\u00fcnwald\u2013Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.<\/jats:p>","DOI":"10.1115\/1.4003136","type":"journal-article","created":{"date-parts":[[2011,3,4]],"date-time":"2011-03-04T11:53:56Z","timestamp":1299239636000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":22,"title":["Generalized Gr\u00fcnwald\u2013Letnikov Fractional Derivative and Its Laplace and Fourier Transforms"],"prefix":"10.1115","volume":"6","author":[{"given":"Manuel D.","family":"Ortigueira","sequence":"first","affiliation":[{"name":"UNINOVA\/DEE, Faculdade de Ci\u00eancias e Tecnologia da Universidade Nova de Lisboa, Campus da FCT da UNL, Quinta da Torre, 2825-114 Monte da Caparica, Portugal"}]},{"given":"Juan J.","family":"Trujillo","sequence":"additional","affiliation":[{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, University La Laguna, La Laguna, 38271 Tenerife, Spain"}]}],"member":"33","published-online":{"date-parts":[[2011,3,2]]},"reference":[{"volume-title":"Theory and Applications of Fractional Differential Equations","author":"Kilbas","key":"2019100313420855100_c1"},{"volume-title":"Fractional Integrals and Derivatives\u2014Theory and Applications","author":"Samko","key":"2019100313420855100_c2"},{"author":"Ortigueira","article-title":"Fractional Differences Integral Representation and Its Use to Define Fractional Differintegrations","key":"2019100313420855100_c3"},{"author":"Ortigueira","article-title":"A New Look at the Differintegration Definition","key":"2019100313420855100_c4"},{"issue":"4","key":"2019100313420855100_c5","first-page":"459","article-title":"From Differences to Differintegrations","volume":"7","author":"Ortigueira","journal-title":"Fractional Calculus Appl. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1311-0454","issn-type":"print"},{"issue":"10","key":"2019100313420855100_c6","doi-asserted-by":"crossref","first-page":"2505","DOI":"10.1016\/j.sigpro.2006.02.002","article-title":"A Coherent Approach to Non Integer Order Derivatives","volume":"86","author":"Ortigueira","journal-title":"Signal Processing"},{"unstructured":"Dugowson, S.\n          , 1994, \u201cLes diff\u00e9rentielles m\u00e9taphysiques,\u201d Ph.D. thesis, Universit\u00e9 Paris Nord, Paris.","key":"2019100313420855100_c7"},{"volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"Miller","key":"2019100313420855100_c8"},{"volume-title":"Fractional Differential Equations","author":"Podlubny","key":"2019100313420855100_c9"},{"volume-title":"Applied and Computational Complex Analysis","author":"Henrici","first-page":"389","key":"2019100313420855100_c10"},{"volume-title":"Signals and Systems","author":"Roberts","key":"2019100313420855100_c11"},{"issue":"1","key":"2019100313420855100_c12","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1049\/ip-vis:20000272","article-title":"Introduction to Fractional Linear Systems. Part 1: Continuous-Time","volume":"147","author":"Ortigueira","journal-title":"IEE Proc. Vision Image Signal Process.","ISSN":"https:\/\/id.crossref.org\/issn\/1350-245X","issn-type":"print"}],"container-title":["Journal of Computational and Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computationalnonlinear\/article-pdf\/doi\/10.1115\/1.4003136\/5590683\/034501_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computationalnonlinear\/article-pdf\/doi\/10.1115\/1.4003136\/5590683\/034501_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T13:42:18Z","timestamp":1570110138000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computationalnonlinear\/article\/doi\/10.1115\/1.4003136\/385001\/Generalized-Gr%C3%BCnwaldLetnikov-Fractional-Derivative"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,2]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,7,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4003136","relation":{},"ISSN":["1555-1415","1555-1423"],"issn-type":[{"type":"print","value":"1555-1415"},{"type":"electronic","value":"1555-1423"}],"subject":[],"published":{"date-parts":[[2011,3,2]]},"article-number":"034501"}}