{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,21]],"date-time":"2024-07-21T05:18:00Z","timestamp":1721539080461},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,4,30]],"date-time":"2015-04-30T00:00:00Z","timestamp":1430352000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM2010--15314 and MTM2013--43014--P"],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Xunta de Galicia","doi-asserted-by":"publisher","award":["R2014\/002"],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/04106\/2013","PTDC\/EEI-AUT\/1450\/2012"],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"FEDER under POFC-QREN","doi-asserted-by":"publisher","award":["FCOMP-01-0124-FEDER-028894"],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10957-015-0743-7","type":"journal-article","created":{"date-parts":[[2015,4,29]],"date-time":"2015-04-29T15:56:25Z","timestamp":1430322985000},"page":"7-31","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations"],"prefix":"10.1007","volume":"174","author":[{"given":"Amar","family":"Debbouche","sequence":"first","affiliation":[]},{"given":"Juan J.","family":"Nieto","sequence":"additional","affiliation":[]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,30]]},"reference":[{"key":"743_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-0457-6","volume-title":"Fractional Dynamics and Control","author":"D Baleanu","year":"2012","unstructured":"Baleanu, D., Tenreiro Machado, J.A., Luo, A.C.J.: Fractional Dynamics and Control. Springer, New York (2012)"},{"key":"743_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations","author":"K Diethelm","year":"2010","unstructured":"Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)"},{"key":"743_CR3","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley-Interscience Publication","author":"KS Miller","year":"1993","unstructured":"Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley-Interscience Publication. Wiley, New York (1993)"},{"key":"743_CR4","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, CA (1999)"},{"key":"743_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14003-7","volume-title":"Fractional Dynamics","author":"VE Tarasov","year":"2010","unstructured":"Tarasov, V.E.: Fractional Dynamics. Springer, Heidelberg (2010)"},{"key":"743_CR6","doi-asserted-by":"crossref","DOI":"10.1142\/9069","volume-title":"Basic Theory of Fractional Differential Equations","author":"Y Zhou","year":"2014","unstructured":"Zhou, Y.: Basic Theory of Fractional Differential Equations. World Scientific, Singapore (2014)"},{"key":"743_CR7","doi-asserted-by":"crossref","first-page":"2859","DOI":"10.1016\/j.na.2009.11.029","volume":"72","author":"RP Agarwal","year":"2010","unstructured":"Agarwal, R.P., Lakshmikantham, V., Nieto, J.J.: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859\u20132862 (2010)","journal-title":"Nonlinear Anal."},{"key":"743_CR8","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/BF02083817","volume":"35","author":"AMA El-Sayed","year":"1996","unstructured":"El-Sayed, A.M.A.: Fractional-order diffusion-wave equation. Int. J. Theor. Phys. 35, 311\u2013322 (1996)","journal-title":"Int. J. Theor. Phys."},{"key":"743_CR9","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.1016\/j.aml.2010.06.007","volume":"23","author":"JJ Nieto","year":"2010","unstructured":"Nieto, J.J.: Maximum principles for fractional differential equations derived from Mittag\u2013Leffler functions. Appl. Math. Lett. 23, 1248\u20131251 (2010)","journal-title":"Appl. Math. Lett."},{"key":"743_CR10","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.chaos.2014.07.001","volume":"67","author":"Y Shen","year":"2014","unstructured":"Shen, Y., Yang, S., Sui, C.: Analysis on limit cycle of fractional-order van der Pol oscillator. Chaos Solitons Fractals 67, 94\u2013102 (2014)","journal-title":"Chaos Solitons Fractals"},{"key":"743_CR11","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1023\/B:JOTA.0000004868.61288.8e","volume":"118","author":"M Benchohra","year":"2003","unstructured":"Benchohra, M., Gatsori, E.P., Ntouyas, S.K.: Controllability results for semilinear evolution inclusions with nonlocal conditions. J. Optim. Theory Appl. 118, 493\u2013513 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"743_CR12","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.1016\/j.camwa.2011.03.075","volume":"62","author":"A Debbouche","year":"2011","unstructured":"Debbouche, A., Baleanu, D.: Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comput. Math. Appl. 62, 1442\u20131450 (2011)","journal-title":"Comput. Math. Appl."},{"key":"743_CR13","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1186\/1687-2770-2012-78","volume":"2012","author":"A Debbouche","year":"2012","unstructured":"Debbouche, A., Baleanu, D., Agarwal, R.P.: Nonlocal nonlinear integrodifferential equations of fractional orders. Bound. Value Probl. 2012, 78 (2012)","journal-title":"Bound. Value Probl."},{"key":"743_CR14","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1080\/00207179.2013.791927","volume":"86","author":"A Debbouche","year":"2013","unstructured":"Debbouche, A., Torres, D.F.M.: Approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces. Int. J. Control 86, 1577\u20131585 (2013)","journal-title":"Int. J. Control"},{"key":"743_CR15","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1016\/j.na.2008.02.087","volume":"70","author":"GM N\u2019Gu\u00e9r\u00e9kata","year":"2009","unstructured":"N\u2019Gu\u00e9r\u00e9kata, G.M.: A Cauchy problem for some fractional abstract differential equation with non local conditions. Nonlinear Anal. 70, 1873\u20131876 (2009)","journal-title":"Nonlinear Anal."},{"key":"743_CR16","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1016\/j.camwa.2011.02.040","volume":"62","author":"J Wang","year":"2011","unstructured":"Wang, J., Zhou, Y., Wei, W., Xu, H.: Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls. Comput. Math. Appl. 62, 1427\u20131441 (2011)","journal-title":"Comput. Math. Appl."},{"key":"743_CR17","doi-asserted-by":"crossref","first-page":"4465","DOI":"10.1016\/j.nonrwa.2010.05.029","volume":"11","author":"Y Zhou","year":"2010","unstructured":"Zhou, Y., Jiao, F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal. Real World Appl. 11, 4465\u20134475 (2010)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"743_CR18","volume-title":"Theory and Applications of Fractional Differential Equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)"},{"key":"743_CR19","doi-asserted-by":"crossref","first-page":"3337","DOI":"10.1016\/j.na.2007.09.025","volume":"69","author":"V Lakshmikantham","year":"2008","unstructured":"Lakshmikantham, V.: Theory of fractional functional differential equations. Nonlinear Anal. 69, 3337\u20133343 (2008)","journal-title":"Nonlinear Anal."},{"key":"743_CR20","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1016\/j.na.2007.08.042","volume":"69","author":"V Lakshmikantham","year":"2008","unstructured":"Lakshmikantham, V., Vatsala, A.S.: Basic theory of fractional differential equations. Nonlinear Anal. 69, 2677\u20132682 (2008)","journal-title":"Nonlinear Anal."},{"key":"743_CR21","volume-title":"Feedback Control of Dynamic Systems","author":"GF Franklin","year":"2014","unstructured":"Franklin, G.F., Da Powell, J., Emami-Naeini, A.: Feedback Control of Dynamic Systems. Prentice Hall, Reading, MA (2014)"},{"key":"743_CR22","doi-asserted-by":"crossref","DOI":"10.1142\/p871","volume-title":"Introduction to the Fractional Calculus of Variations","author":"AB Malinowska","year":"2012","unstructured":"Malinowska, A.B., Torres, D.F.M.: Introduction to the Fractional Calculus of Variations. Imp. Coll. Press, London (2012)"},{"key":"743_CR23","doi-asserted-by":"crossref","DOI":"10.1142\/p991","volume-title":"Computational Methods in the Fractional Calculus of Variations","author":"R Almeida","year":"2015","unstructured":"Almeida, R., Pooseh, S., Torres, D.F.M.: Computational Methods in the Fractional Calculus of Variations. Imp. Coll. Press, London (2015)"},{"key":"743_CR24","volume-title":"Advanced Methods in the Fractional Calculus of Variations. Springer Briefs in Applied Sciences and Technology","author":"AB Malinowska","year":"2015","unstructured":"Malinowska, A.B., Odzijewicz, T., Torres, D.F.M.: Advanced Methods in the Fractional Calculus of Variations. Springer Briefs in Applied Sciences and Technology. Springer, Cham (2015)"},{"key":"743_CR25","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s11071-004-3764-6","volume":"38","author":"OP Agrawal","year":"2004","unstructured":"Agrawal, O.P.: A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 38, 323\u2013337 (2004)","journal-title":"Nonlinear Dyn."},{"key":"743_CR26","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11071-007-9309-z","volume":"53","author":"GSF Frederico","year":"2008","unstructured":"Frederico, G.S.F., Torres, D.F.M.: Fractional conservation laws in optimal control theory. Nonlinear Dyn. 53, 215\u2013222 (2008)","journal-title":"Nonlinear Dyn."},{"key":"743_CR27","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.physleta.2008.11.019","volume":"373","author":"N \u00d6zdemir","year":"2009","unstructured":"\u00d6zdemir, N., Karadeniz, D., \u0130skender, B.B.: Fractional optimal control problem of a distributed system in cylindrical coordinates. Phys. Lett. A 373, 221\u2013226 (2009)","journal-title":"Phys. Lett. A"},{"key":"743_CR28","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s10957-012-0174-7","volume":"156","author":"M Fec\u0306kan","year":"2013","unstructured":"Fec\u0306kan, M., Wang, J., Zhou, Y.: Controllability of fractional functional evolution equations of Sobolev type via characteristic solution operators. J. Optim. Theory Appl. 156, 79\u201395 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"743_CR29","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.jmaa.2012.02.057","volume":"391","author":"F Li","year":"2012","unstructured":"Li, F., Liang, J., Xu, H.-K.: Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions. J. Math. Anal. Appl. 391, 510\u2013525 (2012)","journal-title":"J. Math. Anal. Appl."},{"key":"743_CR30","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.amc.2014.07.073","volume":"245","author":"A Debbouche","year":"2014","unstructured":"Debbouche, A., Nieto, J.J.: Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls. Appl. Math. Comput. 245, 74\u201385 (2014)","journal-title":"Appl. Math. Comput."},{"key":"743_CR31","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.amc.2014.05.087","volume":"243","author":"A Debbouche","year":"2014","unstructured":"Debbouche, A., Torres, D.F.M.: Approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions. Appl. Math. Comput. 243, 161\u2013175 (2014)","journal-title":"Appl. Math. Comput."},{"key":"743_CR32","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.amc.2014.02.086","volume":"235","author":"R Kamocki","year":"2014","unstructured":"Kamocki, R.: On the existence of optimal solutions to fractional optimal control problems. Appl. Math. Comput. 235, 94\u2013104 (2014)","journal-title":"Appl. Math. Comput."},{"key":"743_CR33","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.jmaa.2013.07.032","volume":"409","author":"X Liu","year":"2014","unstructured":"Liu, X., Liu, Z., Fu, X.: Relaxation in nonconvex optimal control problems described by fractional differential equations. J. Math. Anal. Appl. 409, 446\u2013458 (2014)","journal-title":"J. Math. Anal. Appl."},{"key":"743_CR34","volume-title":"Convex Analysis and Variational Problems","author":"I Ekeland","year":"1976","unstructured":"Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976)"},{"key":"743_CR35","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1016\/0960-0779(95)00125-5","volume":"7","author":"F Mainardi","year":"1996","unstructured":"Mainardi, F.: Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 7, 1461\u20131477 (1996)","journal-title":"Chaos Solitons Fractals"},{"key":"743_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","author":"A Pazy","year":"1983","unstructured":"Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)"},{"key":"743_CR37","volume-title":"Abstract Differential Equations","author":"SD Zaidman","year":"1979","unstructured":"Zaidman, S.D.: Abstract Differential Equations. Pitman, Boston, MA (1979)"},{"key":"743_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69512-4","volume-title":"Differential Inclusions","author":"J-P Aubin","year":"1984","unstructured":"Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984)"},{"key":"743_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6359-4","volume-title":"Handbook of Multivalued Analysis","author":"S Hu","year":"1997","unstructured":"Hu, S., Papageorgiou, N.S.: Handbook of Multivalued Analysis, vol. 1. Kluwer, Dordrecht (1997)"},{"key":"743_CR40","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1070\/SM1999v190n11ABEH000441","volume":"190","author":"AA Tolstonogov","year":"1999","unstructured":"Tolstonogov, A.A.: Relaxation in nonconvex optimal control problems described by first-order evolution equations. Sb. Math. 190, 1689\u20131714 (1999)","journal-title":"Sb. Math."},{"key":"743_CR41","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.camwa.2009.06.026","volume":"59","author":"Y Zhou","year":"2010","unstructured":"Zhou, Y., Jiao, F.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59, 1063\u20131077 (2010)","journal-title":"Comput. Math. Appl."},{"key":"743_CR42","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1002\/zamm.19860661107","volume":"66","author":"J Dixon","year":"1986","unstructured":"Dixon, J., McKee, S.: Weakly singular discrete Gronwall inequalities. Z. Angew. Math. Mech. 66, 535\u2013544 (1986)","journal-title":"Z. Angew. Math. Mech."},{"key":"743_CR43","doi-asserted-by":"crossref","first-page":"53","DOI":"10.4064\/fm-87-1-53-72","volume":"87","author":"CJ Himmelberg","year":"1975","unstructured":"Himmelberg, C.J.: Measurable relations. Fund. Math. 87, 53\u201372 (1975)","journal-title":"Fund. Math."},{"key":"743_CR44","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/BF01236303","volume":"48","author":"AA Tolstonogov","year":"1990","unstructured":"Tolstonogov, A.A.: On the Scorza\u2013Dragoni theorem for multivalued mappings with a variable domain. Math. Notes 48, 1151\u20131158 (1990)","journal-title":"Math. Notes"},{"key":"743_CR45","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/S0363012903423156","volume":"43","author":"FS Blasi De","year":"2004","unstructured":"De Blasi, F.S., Pianigiani, G., Tolstonogov, A.A.: A Bogolyubov-type theorem with a nonconvex constraint in Banach spaces. SIAM J. Control Optim. 43, 466\u2013476 (2004)","journal-title":"SIAM J. Control Optim."},{"key":"743_CR46","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0022-0396(91)90011-W","volume":"93","author":"QJ Zhu","year":"1991","unstructured":"Zhu, Q.J.: On the solution set of differential inclusions in Banach space. J. Differ. Equ. 93, 213\u2013237 (1991)","journal-title":"J. Differ. Equ."},{"key":"743_CR47","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF00419367","volume":"4","author":"AA Tolstonogov","year":"1996","unstructured":"Tolstonogov, A.A., Tolstonogov, D.A.: $$L_p$$ L p -continuous extreme selectors of multifunctions with decomposable values: relaxation theorems. Set-Valued Anal. 4, 237\u2013269 (1996)","journal-title":"Set-Valued Anal."},{"key":"743_CR48","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/0362-546X(87)90092-7","volume":"11","author":"EJ Balder","year":"1987","unstructured":"Balder, E.J.: Necessary and sufficient conditions for $$L_1$$ L 1 -strong-weak lower semicontinuity of integral functionals. Nonlinear Anal. 11, 1399\u20131404 (1987)","journal-title":"Nonlinear Anal."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-015-0743-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-015-0743-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-015-0743-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-015-0743-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T17:44:05Z","timestamp":1717868645000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-015-0743-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,30]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["743"],"URL":"https:\/\/doi.org\/10.1007\/s10957-015-0743-7","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,30]]}}}