{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T23:04:17Z","timestamp":1772665457830,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"16-18","license":[{"start":{"date-parts":[[2017,12,1]],"date-time":"2017-12-01T00:00:00Z","timestamp":1512086400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Eur. Phys. J. Spec. Top."],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1140\/epjst\/e2018-00036-0","type":"journal-article","created":{"date-parts":[[2018,7,21]],"date-time":"2018-07-21T05:37:21Z","timestamp":1532151441000},"page":"3489-3499","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Generalized fractional operators on time scales with application to dynamic equations"],"prefix":"10.1140","volume":"226","author":[{"given":"Kheira","family":"Mekhalfi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"2884_CR1","doi-asserted-by":"crossref","unstructured":"S. Abbas, M. Benchohra, G.M. N\u2019Gu\u00e9r\u00e9kata, in Developments in mathematics, Topics in fractional differential equations (Springer, New York, 2012), Vol. 27","DOI":"10.1007\/978-1-4614-4036-9"},{"key":"2884_CR2","unstructured":"E.G. Bajlekova, Fractional evolution equations in Banach spaces (Eindhoven University of Technology, Eindhoven, 2001)"},{"key":"2884_CR3","doi-asserted-by":"publisher","first-page":"3462","DOI":"10.1016\/j.na.2010.07.035","volume":"73","author":"E. Hern\u00e1ndez","year":"2010","unstructured":"E. Hern\u00e1ndez, D. O\u2019Regan, K. Balachandran, Nonlinear Anal. 73, 3462 (2010)","journal-title":"Nonlinear Anal."},{"key":"2884_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-0427(01)00432-0","volume":"141","author":"R. Agarwal","year":"2002","unstructured":"R. Agarwal, M. Bohner, D. O\u2019Regan, A. Peterson, J. Comput. Appl. Math. 141, 1 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"2884_CR5","unstructured":"B. Aulbach, S. Hilger, A unified approach to continuous and discrete dynamics, in Qualitative theory of differential equations (Szeged, 1988), Colloq. Math. Soc. (J\u00e1nos Bolyai, 53, North-Holland, Amsterdam, 1990), p. 37"},{"key":"2884_CR6","doi-asserted-by":"crossref","unstructured":"M. Bohner, A. Peterson, Dynamic equations on time scales (Birkh\u00e4user Boston, Inc., Boston, MA, 2001)","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"2884_CR7","unstructured":"N.R.O. Bastos, Fractional calculus on time scales, PhD thesis (under supervision of D.F.M. Torres), University of Aveiro, 2012"},{"key":"2884_CR8","doi-asserted-by":"publisher","first-page":"417","DOI":"10.3934\/dcds.2011.29.417","volume":"29","author":"N.R.O. Bastos","year":"2011","unstructured":"N.R.O. Bastos, R.A.C. Ferreira, D.F.M. Torres, Discrete Contin. Dyn. Syst. 29, 417 (2011)","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"2884_CR9","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1016\/j.sigpro.2010.05.001","volume":"91","author":"N.R.O. Bastos","year":"2011","unstructured":"N.R.O. Bastos, R.A.C. Ferreira, D.F.M. Torres, Signal Process. 91, 513 (2011)","journal-title":"Signal Process."},{"key":"2884_CR10","first-page":"1","volume":"11","author":"N.R.O. Bastos","year":"2011","unstructured":"N.R.O. Bastos, D. Mozyrska, D.F.M. Torres, Int. J. Math. Comput. 11, 1 (2011)","journal-title":"Int. J. Math. Comput."},{"key":"2884_CR11","doi-asserted-by":"crossref","unstructured":"B. Bayour, D.F.M. Torres, Complex-valued fractional derivatives on time scales, in Differential and difference equations with applications, Springer Proc. Math. Stat. (Springer, Cham, 2016), Vol. 164, p. 79","DOI":"10.1007\/978-3-319-32857-7_8"},{"key":"2884_CR12","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.sigpro.2014.05.026","volume":"107","author":"N. Benkhettou","year":"2015","unstructured":"N. Benkhettou, A.M.C. Brito da Cruz, D.F.M. Torres, Signal Process. 107, 230 (2015)","journal-title":"Signal Process."},{"key":"2884_CR13","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/mma.3475","volume":"39","author":"N. Benkhettou","year":"2016","unstructured":"N. Benkhettou, A.M.C. Brito da Cruz, D.F.M. Torres, Math. Methods Appl. Sci. 39, 261 (2016)","journal-title":"Math. Methods Appl. Sci."},{"key":"2884_CR14","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.jksus.2015.05.003","volume":"28","author":"N. Benkhettou","year":"2016","unstructured":"N. Benkhettou, S. Hassani, D.F.M. Torres, J. King Saud Univ. Sci. 28, 93 (2016)","journal-title":"J. King Saud Univ. Sci."},{"key":"2884_CR15","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/s40065-016-0160-2","volume":"6","author":"E.R. Nwaeze","year":"2017","unstructured":"E.R. Nwaeze, D.F.M. Torres, Arab. J. Math. (Springer) 6, 13 (2017)","journal-title":"Arab. J. Math. (Springer)"},{"key":"2884_CR16","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1186\/s13662-017-1077-6","volume":"2017","author":"M. Sun","year":"2017","unstructured":"M. Sun, C. Hou, Adv. Differ. Equ. 2017, 18 (2017)","journal-title":"Adv. Differ. Equ."},{"key":"2884_CR17","first-page":"1","volume":"6","author":"I. Yaslan","year":"2016","unstructured":"I. Yaslan, O. Liceli, Fract. Differ. Calc. 6, 1 (2016)","journal-title":"Fract. Differ. Calc."},{"key":"2884_CR18","first-page":"247","volume":"42","author":"R.A. Yan","year":"2016","unstructured":"R.A. Yan, S.R. Sun, Z.L. Han, Bull. Iran. Math. Soc. 42, 247 (2016)","journal-title":"Bull. Iran. Math. Soc."},{"key":"2884_CR19","doi-asserted-by":"publisher","first-page":"275","DOI":"10.14317\/jami.2015.275","volume":"33","author":"Z.-J. Gao","year":"2015","unstructured":"Z.-J. Gao, X.-Y. Fu, Q.-L. Li, J. Appl. Math. Inform. 33, 275 (2015)","journal-title":"J. Appl. Math. Inform."},{"key":"2884_CR20","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1155\/2015\/486054","volume":"2015","author":"J. Zhu","year":"2015","unstructured":"J. Zhu, L. Wu, Abstr. Appl. Anal. 2015, 23 (2015)","journal-title":"Abstr. Appl. Anal."},{"key":"2884_CR21","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1142\/S179352451350023X","volume":"6","author":"S.-L. Gao","year":"2013","unstructured":"S.-L. Gao, Int. J. Biomath. 6, 11 (2013)","journal-title":"Int. J. Biomath."},{"key":"2884_CR22","doi-asserted-by":"crossref","unstructured":"R. Hilfer, Applications of fractional calculus in physics (World Scientific Publishing Co., Inc., River Edge, NJ, 2000)","DOI":"10.1142\/9789812817747"},{"key":"2884_CR23","first-page":"2","volume":"2013","author":"S. Sun","year":"2013","unstructured":"S. Sun, T. Abdeljawad, J. Alzabut, Discrete Dyn. Nat. Soc. 2013, 2 (2013)","journal-title":"Discrete Dyn. Nat. Soc."},{"key":"2884_CR24","unstructured":"A. Chidouh, A. Guezane-Lakoud, R. Bebbouchi, A. Bouaricha, D.F.M. Torres, Linear and nonlinear fractional Voigt models, in Theory and Applications of Non-integer Order Systems, Springer, Lecture Notes in Electrical Engineering (2017), Vol. 407, p. 157"},{"key":"2884_CR25","doi-asserted-by":"publisher","first-page":"4682","DOI":"10.1016\/j.cnsns.2011.01.026","volume":"16","author":"T. Abdeljawad","year":"2011","unstructured":"T. Abdeljawad, D. Baleanu, Commun. Nonlinear Sci. Numer. Simul. 16, 4682 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2884_CR26","first-page":"149","volume":"44","author":"J. JaganMohan","year":"2014","unstructured":"J. JaganMohan, Novi Sad J. Math. 44, 149 (2014)","journal-title":"Novi Sad J. Math."},{"key":"2884_CR27","doi-asserted-by":"publisher","unstructured":"M.R. Sidi Ammi, D.F.M. Torres, J. King Saud Univ. Sci. (2017), DOI: https:\/\/doi.org\/10.1016\/j.jksus.2017.03.004 (in press)","DOI":"10.1016\/j.jksus.2017.03.004"},{"key":"2884_CR28","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jksus.2015.08.001","volume":"28","author":"N. Benkhettou","year":"2016","unstructured":"N. Benkhettou, A. Hammoudi, D.F.M. Torres, J. King Saud Univ. Sci. 28, 87 (2016)","journal-title":"J. King Saud Univ. Sci."},{"key":"2884_CR29","doi-asserted-by":"crossref","unstructured":"B. Aulbach, S. Hilger, in Nonlinear dynamics and quantum dynamical systems (Gaussig, 1990), Math. Res. (Akademie-Verlag, Berlin, 1990), Vol. 59, p. 9","DOI":"10.1515\/9783112581445-002"},{"key":"2884_CR30","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/BF03323153","volume":"18","author":"S. Hilger","year":"1990","unstructured":"S. Hilger, Results Math. 18, 18 (1990)","journal-title":"Results Math."},{"key":"2884_CR31","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/BF03322019","volume":"35","author":"R.P. Agarwal","year":"1999","unstructured":"R.P. Agarwal, M. Bohner, Results Math. 35, 3 (1999)","journal-title":"Results Math."},{"key":"2884_CR32","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0022-247X(03)00361-5","volume":"285","author":"G.Sh. Guseinov","year":"2003","unstructured":"G.Sh. Guseinov, J. Math. Anal. Appl. 285, 107 (2003)","journal-title":"J. Math. Anal. Appl."},{"key":"2884_CR33","first-page":"14","volume":"7","author":"D. Mozyrska","year":"2010","unstructured":"D. Mozyrska, E. Paw\u0142uszewicz, D.F.M. Torres, Aust. J. Math. Anal. Appl. 7, 14 (2010)","journal-title":"Aust. J. Math. Anal. Appl."},{"key":"2884_CR34","first-page":"241","volume":"38","author":"A. Ahmadkhanlu","year":"2012","unstructured":"A. Ahmadkhanlu, M. Jahanshahi, Bull. Iran. Math. Soc. 38, 241 (2012)","journal-title":"Bull. Iran. Math. Soc."},{"key":"2884_CR35","unstructured":"S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivatives, translated from the 1987 Russian original (Gordon and Breach Science Publishers, Yverdon, 1993)"},{"key":"2884_CR36","doi-asserted-by":"crossref","unstructured":"A. Granas, J. Dugundji, Fixed point theory, Springer monographs in mathematics (Springer-Verlag, New York, 2003)","DOI":"10.1007\/978-0-387-21593-8"}],"container-title":["The European Physical Journal Special Topics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1140\/epjst\/e2018-00036-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1140\/epjst\/e2018-00036-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1140\/epjst\/e2018-00036-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,28]],"date-time":"2022-08-28T01:01:40Z","timestamp":1661648500000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1140\/epjst\/e2018-00036-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12]]},"references-count":36,"journal-issue":{"issue":"16-18","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["2884"],"URL":"https:\/\/doi.org\/10.1140\/epjst\/e2018-00036-0","relation":{},"ISSN":["1951-6355","1951-6401"],"issn-type":[{"value":"1951-6355","type":"print"},{"value":"1951-6401","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12]]},"assertion":[{"value":"20 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}