{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T01:03:04Z","timestamp":1725584584773},"publisher-location":"Dordrecht","reference-count":38,"publisher":"Springer Netherlands","isbn-type":[{"type":"print","value":"9789400707467"},{"type":"electronic","value":"9789400707474"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-94-007-0747-4_4","type":"book-chapter","created":{"date-parts":[[2011,6,1]],"date-time":"2011-06-01T08:39:12Z","timestamp":1306917552000},"page":"71-99","source":"Crossref","is-referenced-by-count":0,"title":["Fractional Linear Shift-Invariant Systems"],"prefix":"10.1007","author":[{"given":"Manuel Duarte","family":"Ortigueira","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,6,2]]},"reference":[{"key":"4_CR1","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1002\/eqe.4290190207","volume":"19","author":"CG Koh","year":"1990","unstructured":"Koh CG, Kelly JM (1990) Application of fractional derivatives to seismic analysis of basedisolated models. Earthq Eng Struct D 19:229\u2013241","journal-title":"Earthq Eng Struct D"},{"key":"4_CR2","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF00206239","volume":"72","author":"TJ Anastasio","year":"1994","unstructured":"Anastasio TJ (1994) The fractional-order dynamics of brainstem vestibulo-ocular dynamics of brainstem vestibular-oculomotor neurons. Biol Cybern 72:69\u201379","journal-title":"Biol Cybern"},{"issue":"2","key":"4_CR3","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0888-3270(91)90016-X","volume":"5","author":"L Gaul","year":"1991","unstructured":"Gaul L, Klein P, Kemple S (1991) Damping description involving fractional operators. Mech Syst Signal Process 5(2):81\u201388","journal-title":"Mech Syst Signal Process"},{"issue":"9","key":"4_CR4","doi-asserted-by":"publisher","first-page":"2708","DOI":"10.1061\/(ASCE)0733-9445(1991)117:9(2708)","volume":"117","author":"N Makris","year":"1991","unstructured":"Makris N, Constantinou MC (1991) Fractional-derivative Maxwell model for viscous dampers. J Struct Eng 117(9):2708\u20132724","journal-title":"J Struct Eng"},{"key":"4_CR5","doi-asserted-by":"crossref","unstructured":"Clerc JP, Tremblay A-MS, Albinet G, Mitescu, CD (1984) a. c. Response of Fractal Networks. Le Journal de Physique-Lettres 45(19)","DOI":"10.1051\/jphyslet:019840045019091300"},{"issue":"10","key":"4_CR6","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1109\/TCS.1981.1084917","volume":"28","author":"A Oustaloup","year":"1981","unstructured":"Oustaloup A (1981) Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation. IEEE Trans Circuits Syst 28(10):1007\u20131009","journal-title":"IEEE Trans Circuits Syst"},{"key":"4_CR7","unstructured":"Matignon D, d' Andr\u00e9a-Novel B (1995) D\u00e9composition modale fractionaire de l\u00b4 \u00e9quation des ondes avec pertes viscothermiques, Tech. Rep. 95 C 001, \u00c9cole Nationale Sup\u00e9rieure des T\u00e9l\u00e9communications"},{"issue":"2","key":"4_CR8","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0947-3580(95)70014-0","volume":"1","author":"A Oustaloup","year":"1995","unstructured":"Oustaloup A, Mathieu B, Lanusse P (1995) The CRONE control of resonant plants: application to a flexible transmission. Eur J Control 1(2):113\u2013121","journal-title":"Eur J Control"},{"key":"4_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-6042-7","volume-title":"Advances in fractional calculus: theoretical developments and applications in physics and engineering","author":"JM Sabatier","year":"2007","unstructured":"Sabatier JM, Agrawal OP, Machado JAT (2007) Advances in fractional calculus: theoretical developments and applications in physics and engineering. Springer, Berlin"},{"key":"4_CR10","unstructured":"Machado JAT, Azenha A (1998) Position\/Force fractional control of mechanical manipulators. In: Proceedings of the 1998 5th international workshop on advanced motion control, Coimbra, Portugal, pp. 216\u2013221"},{"key":"4_CR11","unstructured":"Magin RL (2006) Fractional calculus in bioengineering. Begell House, Connecticut"},{"key":"4_CR12","first-page":"251","volume":"44","author":"D Craiem","year":"2007","unstructured":"Craiem D, Armentano RL (2007) A fractional derivative model to describe arterial viscoelasticity. Biorheology 44:251\u2013263","journal-title":"Biorheology"},{"issue":"2","key":"4_CR13","first-page":"115","volume":"26","author":"NA Kolmogorov","year":"1940","unstructured":"Kolmogorov NA (1940) Wienersche Spiralen und Einige Andere Interessante Kurven im Hilbertschen Raum. Compte Rendus de l\u2019Acad\u00e9mie des Sciences de 1\u2019Union des R\u00e9publiques Sovi\u00e9tiques Socialistes 26(2):115\u2013118","journal-title":"Compte Rendus de l\u2019Acad\u00e9mie des Sciences de 1\u2019Union des R\u00e9publiques Sovi\u00e9tiques Socialistes"},{"issue":"4","key":"4_CR14","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1137\/1010093","volume":"10","author":"BB Mandelbrot","year":"1968","unstructured":"Mandelbrot BB, Van Ness JW (1968) The fractional Brownian motions, fractional noises and applications. SIAM Rev 10(4):422\u2013437","journal-title":"SIAM Rev"},{"issue":"7","key":"4_CR15","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1016\/j.physleta.2007.08.062","volume":"372","author":"MD Ortigueira","year":"2008","unstructured":"Ortigueira MD, Batista AG (2008) On the relation between the fractional Brownian motion and the fractional derivatives. Phys Lett A 372(7):958\u2013968","journal-title":"Phys Lett A"},{"key":"4_CR16","doi-asserted-by":"crossref","unstructured":"Ortigueira MD (2000) Introduction to fractional signal processing. Part 1: continuous-time systems. In: IEE proceedings on vision, image and signal processing, no 1, February, pp 62\u201370","DOI":"10.1049\/ip-vis:20000272"},{"key":"4_CR17","unstructured":"Henrici P (1991) Applied and computational complex analysis, vol 2. Wiley, New York, pp 389\u2013391"},{"key":"4_CR18","volume-title":"Theory and applications of fractional differential equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam"},{"key":"4_CR19","unstructured":"Lundberg HK, Miller HR, Trumper DL (2007) Initial conditions, generalized functions, and the Laplace transform: Troubles at the origin. IEEE Control Sys Mag pp. 22\u201335"},{"key":"4_CR20","unstructured":"Ferreira JC (1997) Introduction to the theory of distributions. Pitman monographs and surveys in pure and applied mathematics, July"},{"key":"4_CR21","volume-title":"Delta Functions","author":"RF Hoskins","year":"1999","unstructured":"Hoskins RF (1999). Delta Functions. Horwood Series in Mathematics & Applications. Chichester, England"},{"key":"4_CR22","unstructured":"Samko SG, Kilbas AA, Marichev OI (1987) Fractional integrals and derivatives\u2014theory and applications. Gordon and Breach Science Publishers, New York"},{"key":"4_CR23","unstructured":"Miller KS, Ross B (1993) An introduction to the fractional calculus and fractional differential equations. Wiley, New York"},{"key":"4_CR24","unstructured":"Podlubny I (1999) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, San Diego"},{"key":"4_CR25","first-page":"108","volume":"23","author":"M Davison","year":"1998","unstructured":"Davison M, Essex C (1998) Fractional differential equations and initial value problems. Math. Scil 23:108\u2013116","journal-title":"Math. Scil"},{"issue":"1","key":"4_CR26","first-page":"51","volume":"141","author":"F Mainardi","year":"2003","unstructured":"Mainardi F, Pagnini G (2003). The Wright functions as solutions of the time-fractional diffusion equation. JAMC 141:(1) 51\u201362","journal-title":"JAMC"},{"key":"4_CR27","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1016\/j.jmaa.2005.05.009","volume":"316","author":"V Daftardar-Gejji","year":"2006","unstructured":"Daftardar-Gejji V, Jafari H (2006) An iterative method for solving nonlinear functional equations. J Math Anal Appl 316:753\u2013763","journal-title":"J Math Anal Appl"},{"key":"4_CR28","first-page":"1","volume":"37","author":"N Heymans","year":"2005","unstructured":"Heymans N, Podlubny I (2005) Physical interpretation of initial conditions for fractional differential equations with Riemann\u2013Liouville fractional derivatives. Rheol Acta 37:1\u20137","journal-title":"Rheol Acta"},{"key":"4_CR29","doi-asserted-by":"publisher","first-page":"10375","DOI":"10.1088\/0305-4470\/39\/33\/008","volume":"39","author":"O Agrawal","year":"2006","unstructured":"Agrawal O (2006) Fractional variational calculus and the transversality conditions. J Phys A: Math Gen 39:10375\u201310384","journal-title":"J Phys A: Math Gen"},{"key":"4_CR30","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-7091-2664-6_5","volume-title":"Fractals and fractional calculus in continuum mechanics","author":"R Gorenflo","year":"1997","unstructured":"Gorenflo R, Mainardi F (1997) Integral and differential equations of fractional order. In: Carpinteri A, Mainardi F (eds) Fractals and fractional calculus in continuum mechanics. Springer Verlag, New York, pp 223\u2013276"},{"issue":"9","key":"4_CR31","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.amc.2006.08.104","volume":"187","author":"B Bonilla","year":"2007","unstructured":"Bonilla B, Rivero M, Trujillo JJ (2007) On systems of linear fractional differential equations with constant coefficients. Appl Math Comp 187(9):68\u201378","journal-title":"Appl Math Comp"},{"issue":"11","key":"4_CR32","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1016\/S0165-1684(03)00183-X","volume":"83","author":"MD Ortigueira","year":"2003","unstructured":"Ortigueira MD (2003) On the initial conditions in continuous-time fractional linear systems. Signal Processing 83(11):2301\u20132309","journal-title":"Signal Processing"},{"key":"4_CR33","unstructured":"Ortigueira MD, Coito FJ (2010) System initial conditions vs Derivative initial conditions, computers and mathematics with applications. Special issue on fractional differentiation and Its applications, Vol. 59(5): pp. 1782\u20131789"},{"key":"4_CR34","unstructured":"Ortigueira MD, Coito FJ (2008) Initial conditions: what are we talking about?. In: Proceedings of the 3rd IFAC workshop on fractional differentiation and its applications. Ankara, Turkey, 5\u20137 Nov 2008"},{"issue":"1","key":"4_CR35","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/S0378-7753(00)00488-2","volume":"91","author":"PJ Mahon","year":"2000","unstructured":"Mahon PJ, Paul GL, Kesshishian SM, Vassallo AM (2000) Measurement and modelling of high-power performance of carbon-based supercapacitors. J Power Sources 91(1):68\u201376","journal-title":"J Power Sources"},{"issue":"6","key":"4_CR36","doi-asserted-by":"publisher","first-page":"641","DOI":"10.2116\/analsci.18.641","volume":"18","author":"M Itagaki","year":"2002","unstructured":"Itagaki M, Taya A, Watanabe K, Noda K (2002) Deviations of capacitive and inductive loops in the electrochemical impedance of a dissolving iron electrode. Anal Sci 18(6):641\u2013644","journal-title":"Anal Sci"},{"key":"4_CR37","volume-title":"Dead matter has memory","author":"S Westerlund","year":"2002","unstructured":"Westerlund S (2002) Dead matter has memory. Causal Consulting, Kalmar"},{"key":"4_CR38","volume-title":"Distribution theory and transform analysis","author":"AH Zemanian","year":"1987","unstructured":"Zemanian AH (1987) Distribution theory and transform analysis. Dover Publications, New York"}],"container-title":["Lecture Notes in Electrical Engineering","Fractional Calculus for Scientists and Engineers"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-94-007-0747-4_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,11]],"date-time":"2019-06-11T06:07:36Z","timestamp":1560233256000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-94-007-0747-4_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9789400707467","9789400707474"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-94-007-0747-4_4","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2011]]}}}