{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T15:37:07Z","timestamp":1725982627617},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319940052"},{"type":"electronic","value":"9783319940069"}],"license":[{"start":{"date-parts":[[2018,6,30]],"date-time":"2018-06-30T00:00:00Z","timestamp":1530316800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-319-94006-9_4","type":"book-chapter","created":{"date-parts":[[2018,6,29]],"date-time":"2018-06-29T08:14:15Z","timestamp":1530260055000},"page":"61-113","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Fractional Calculus of Variations"],"prefix":"10.1007","author":[{"given":"Ricardo","family":"Almeida","sequence":"first","affiliation":[]},{"given":"Dina","family":"Tavares","sequence":"additional","affiliation":[]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,30]]},"reference":[{"issue":"4","key":"4_CR1","doi-asserted-by":"publisher","first-page":"1515","DOI":"10.1007\/s40840-015-0248-4","volume":"39","author":"R Almeida","year":"2016","unstructured":"Almeida R (2016) Fractional variational problems depending on indefinite integrals and with delay. Bull Malay Math Sci Soc 39(4):1515\u20131528","journal-title":"Bull Malay Math Sci Soc"},{"issue":"8","key":"4_CR2","doi-asserted-by":"publisher","first-page":"2367","DOI":"10.3934\/dcdsb.2014.19.2367","volume":"19","author":"R Almeida","year":"2014","unstructured":"Almeida R, Malinowska AB (2014) Fractional variational principle of Herglotz. Discret Contin Dyn Syst Ser B 19(8):2367\u20132381","journal-title":"Discret Contin Dyn Syst Ser B"},{"issue":"31","key":"4_CR3","doi-asserted-by":"publisher","first-page":"315403","DOI":"10.1088\/1751-8113\/41\/31\/315403","volume":"41","author":"D Baleanu","year":"2008","unstructured":"Baleanu D, Maaraba T, Jarad F (2008) Fractional variational principles with delay. J Phys A 41(31):315403 8\u00a0pp","journal-title":"J Phys A"},{"key":"4_CR4","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.sigpro.2014.09.026","volume":"107","author":"MC Caputo","year":"2015","unstructured":"Caputo MC, Torres DFM (2015) Duality for the left and right fractional derivatives. Signal Process 107:265\u2013271","journal-title":"Signal Process"},{"key":"4_CR5","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1515\/fca-2015-0026","volume":"16","author":"V Daftardar-Gejji","year":"2015","unstructured":"Daftardar-Gejji V, Sukale Y, Bhalekar S (2015) Solving fractional delay differential equations: A new approach. Fract Calc Appl Anal 16:400\u2013418","journal-title":"Fract Calc Appl Anal"},{"issue":"4","key":"4_CR6","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s11071-006-9094-0","volume":"48","author":"W Deng","year":"2007","unstructured":"Deng W, Li C, L\u00fc J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409\u2013416","journal-title":"Nonlinear Dyn"},{"issue":"2","key":"4_CR7","doi-asserted-by":"publisher","first-page":"261","DOI":"10.12775\/TMNA.2002.036","volume":"20","author":"B Georgieva","year":"2002","unstructured":"Georgieva B, Guenther RB (2002) First Noether-type theorem for the generalized variational principle of Herglotz. Topol Methods Nonlinear Anal 20(2):261\u2013273","journal-title":"Topol Methods Nonlinear Anal"},{"issue":"9","key":"4_CR8","doi-asserted-by":"publisher","first-page":"3911","DOI":"10.1063\/1.1597419","volume":"44","author":"B Georgieva","year":"2003","unstructured":"Georgieva B, Guenther RB, Bodurov T (2003) Generalized variational principle of Herglotz for several independent variables. J Math Phys 44(9):3911\u20133927","journal-title":"J Math Phys"},{"issue":"2","key":"4_CR9","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1137\/1038042","volume":"38","author":"RB Guenther","year":"1996","unstructured":"Guenther RB, Gottsch JA, Kramer DB (1996) The Herglotz algorithm for constructing canonical transformations. SIAM Rev 38(2):287\u2013293","journal-title":"SIAM Rev"},{"key":"4_CR10","unstructured":"Guenther RB, Guenther CM, Gottsch JA (1996) The Herglotz lectures on contact transformations and hamiltonian systems, vol 1. Lecture notes in nonlinear analysis. Juliusz Schauder Center for Nonlinear Studies, Nicholas Copernicus University, Tor\u00fan"},{"key":"4_CR11","unstructured":"Herglotz G (1930) Ber\u00fchrungstransformationen. Lectures at the University of G\u00f6ttingen, G\u00f6ttingen"},{"issue":"1","key":"4_CR12","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/S0034-4877(10)00010-8","volume":"65","author":"F Jarad","year":"2010","unstructured":"Jarad F, Abdeljawad T, Baleanu D (2010) Fractional variational principles with delay within Caputo derivatives. Rep Math Phys 65(1):17\u201328","journal-title":"Rep Math Phys"},{"issue":"3\u20134","key":"4_CR13","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.mcm.2008.09.011","volume":"49","author":"MP Lazarevi\u0107","year":"2009","unstructured":"Lazarevi\u0107 MP, Spasi\u0107 AM (2009) Finite-time stability analysis of fractional order time-delay systems: Gronwall\u2019s approach. Math Comput Model 49(3\u20134):475\u2013481","journal-title":"Math Comput Model"},{"key":"4_CR14","series-title":"A gentle introduction to numerical simulations with MATLAB\/Octave","volume-title":"Programming for computations\u2013MATLAB\/Octave","author":"S Linge","year":"2016","unstructured":"Linge S, Langtangen HP (2016) Programming for computations\u2013MATLAB\/Octave. A gentle introduction to numerical simulations with MATLAB\/Octave. Springer, Cham"},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"Machado JAT (2011) Time-delay and fractional derivatives. Adv Differ Equ 2011:934094. 12\u00a0pp","DOI":"10.1155\/2011\/934094"},{"key":"4_CR16","series-title":"Springer briefs in applied sciences and technology","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-14756-7","volume-title":"Advanced methods in the fractional calculus of variations","author":"AB Malinowska","year":"2015","unstructured":"Malinowska AB, Odzijewicz T, Torres DFM (2015) Advanced methods in the fractional calculus of variations. Springer briefs in applied sciences and technology. Springer, Cham"},{"issue":"4","key":"4_CR17","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s10013-013-0048-9","volume":"42","author":"SPS Santos","year":"2014","unstructured":"Santos SPS, Martins N, Torres DFM (2014) Higher-order variational problems of Herglotz type. Vietnam J Math 42(4):409\u2013419","journal-title":"Vietnam J Math"},{"issue":"9","key":"4_CR18","doi-asserted-by":"publisher","first-page":"4593","DOI":"10.3934\/dcds.2015.35.4593","volume":"35","author":"Sim\u00e3o P. S. Santos","year":"2015","unstructured":"Santos SPS, Martins N, Torres DFM (2015) Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether\u2019s first theorem. Discret Contin Dyn Syst 35(9):4593\u20134610","journal-title":"Discrete and Continuous Dynamical Systems"},{"key":"4_CR19","first-page":"107","volume-title":"Communications in Computer and Information Science","author":"Sim\u00e3o P. S. Santos","year":"2015","unstructured":"Santos SPS, Martins N, Torres DFM (2015) An optimal control approach to Herglotz variational problems. In: Plakhov A, Tchemisova T, Freitas A (eds) Optimization in the natural sciences, Communications in computer and information science, Vol. 499. Springer, pp 107\u2013117"},{"issue":"6","key":"4_CR20","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.1080\/02331934.2015.1010088","volume":"64","author":"D Tavares","year":"2015","unstructured":"Tavares D, Almeida R, Torres DFM (2015) Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order. Optimization 64(6):1381\u20131391","journal-title":"Optimization"},{"issue":"1","key":"4_CR21","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1109\/JAS.2017.7510331","volume":"4","author":"D Tavares","year":"2017","unstructured":"Tavares D, Almeida R, Torres DFM (2017) Constrained fractional variational problems of variable order. IEEE\/CAA Jl Autom Sinica 4(1):80\u201388","journal-title":"IEEE\/CAA Jl Autom Sinica"},{"issue":"1","key":"4_CR22","doi-asserted-by":"publisher","first-page":"143","DOI":"10.3934\/dcdss.2018009","volume":"11","author":"Dina Tavares","year":"2017","unstructured":"Tavares D, Almeida R, Torres DFM (2018) Fractional Herglotz variational problem of variable order. Discret Contin Dyn Syst Ser S 11(1):143\u2013154","journal-title":"Discrete and Continuous Dynamical Systems - Series S"},{"key":"4_CR23","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1016\/j.cam.2017.04.042","volume":"339","author":"Dina Tavares","year":"2018","unstructured":"Tavares D, Almeida R, Torres DFM (2018) Combined fractional variational problems of variable order and some computational aspects. J Comput Appl Math 339:374\u2013388","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"4_CR24","unstructured":"Trefethen LN (2013) Approximation theory and approximation practice. Society for industrial and applied mathematics"},{"key":"4_CR25","series-title":"Universitext","doi-asserted-by":"publisher","DOI":"10.1007\/b97436","volume-title":"The calculus of variations","author":"B Brunt van","year":"2004","unstructured":"van Brunt B (2004) The calculus of variations. Universitext. Springer, New York"},{"issue":"2","key":"4_CR26","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s11063-014-9368-3","volume":"42","author":"H Wang","year":"2015","unstructured":"Wang H, Yu Y, Wen G, Zhang S (2015) Stability analysis of fractional order neural networks with time delay. Neural Process Lett 42(2):479\u2013500","journal-title":"Neural Process Lett"}],"container-title":["SpringerBriefs in Applied Sciences and Technology","The Variable-Order Fractional Calculus of Variations"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-94006-9_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T18:43:31Z","timestamp":1661539411000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-94006-9_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,30]]},"ISBN":["9783319940052","9783319940069"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-94006-9_4","relation":{},"ISSN":["2191-530X","2191-5318"],"issn-type":[{"type":"print","value":"2191-530X"},{"type":"electronic","value":"2191-5318"}],"subject":[],"published":{"date-parts":[[2018,6,30]]}}}