{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,22]],"date-time":"2025-12-22T04:18:14Z","timestamp":1766377094457,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T00:00:00Z","timestamp":1656115200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T00:00:00Z","timestamp":1656115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10957-022-02059-2","type":"journal-article","created":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T15:02:54Z","timestamp":1656169374000},"page":"79-101","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations"],"prefix":"10.1007","volume":"195","author":[{"given":"Yao-Qun","family":"Wu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5283-585X","authenticated-orcid":false,"given":"Jia Wei","family":"He","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,25]]},"reference":[{"key":"2059_CR1","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF01171449","volume":"159","author":"TM Atanackovic","year":"2002","unstructured":"Atanackovic, T.M.: A generalized model for the uniaxial isothermal deformation of a viscoelastic body. Acta Mech. 159, 77\u201386 (2002)","journal-title":"Acta Mech."},{"key":"2059_CR2","doi-asserted-by":"publisher","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 $$L_1$$-strong weak lower semicontinuity of integral functionals. Nonlinear Anal. 11, 1399\u20131404 (1987)","journal-title":"Nonlinear Anal."},{"key":"2059_CR3","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1007\/s10957-018-1314-5","volume":"182","author":"Y Chang","year":"2019","unstructured":"Chang, Y., Pei, Y., Ponce, R.: Existence and optimal controls for fractional stochastic evolution equations of Sobolev type via fractional resolvent operators. J. Optim. Theory Appl. 182, 558\u2013572 (2019)","journal-title":"J. Optim. Theory Appl."},{"key":"2059_CR4","first-page":"74","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":"2059_CR5","doi-asserted-by":"publisher","DOI":"10.1515\/9783110293562","volume-title":"Solutions Set for Differential Equations and Inclusions","author":"S Djebali","year":"2013","unstructured":"Djebali, S., G\u00f3rniewicz, L., Ouahab, A.: Solutions Set for Differential Equations and Inclusions. De Gruyter, Berlin (2013)"},{"issue":"5\u20131","key":"2059_CR6","first-page":"66","volume":"6","author":"MM El-Borai","year":"2017","unstructured":"El-Borai, M.M., Abdou, M.A., Elsayed, M.T.: Optimal control of a class of parabolic partial fractional differential equations. Am. J. Theor. Appl. Stat. 6(5\u20131), 66\u201370 (2017)","journal-title":"Am. J. Theor. Appl. Stat."},{"issue":"2","key":"2059_CR7","first-page":"161","volume":"20","author":"Z Fan","year":"2013","unstructured":"Fan, Z., Mophou, G.: Existence and optimal controls for fractional evolution equations. Nonlinear Stud. 20(2), 161\u2013170 (2013)","journal-title":"Nonlinear Stud."},{"issue":"1","key":"2059_CR8","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10957-012-0174-7","volume":"156","author":"M Feckan","year":"2013","unstructured":"Feckan, M., Wang, J.R., Zhou, Y.: Controllability of fractional functional evolution equations of Sobolev type via characteristic solution operators. J. Optim. Theory Appl. 156(1), 79\u201395 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"2059_CR9","first-page":"344","volume":"257","author":"HB Gu","year":"2015","unstructured":"Gu, H.B., Trujillo, J.J.: Existence of mild solution for evolution equation with Hilfer fractional derivative. Appl. Math. Comput. 257, 344\u2013354 (2015)","journal-title":"Appl. Math. Comput."},{"key":"2059_CR10","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1515\/anona-2021-0211","volume":"11","author":"JW He","year":"2022","unstructured":"He, J.W., Zhou, Y., Peng, L., Ahmad, B.: On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on $$R^N$$. Adv. Nonlinear Anal. 11, 580\u2013597 (2022)","journal-title":"Adv. Nonlinear Anal."},{"issue":"3","key":"2059_CR11","first-page":"299","volume":"12","author":"R Hilfer","year":"2009","unstructured":"Hilfer, R., Luchko, Y., Tomovski, Z.: Operational method for the solution of fractional differential equations with generalized Riemann\u2013Liouville fractional derivatives. Fract. Calc. Appl. Anal. 12(3), 299\u2013318 (2009)","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"3","key":"2059_CR12","doi-asserted-by":"publisher","first-page":"773","DOI":"10.3934\/ipi.2018033","volume":"12","author":"J Jia","year":"2018","unstructured":"Jia, J., Peng, J., Gao, J., Li, Y.: Backward problem for a time-space fractional diffusion equation. Inverse Probl. Imaging 12(3), 773\u2013800 (2018)","journal-title":"Inverse Probl. Imaging"},{"key":"2059_CR13","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":"2059_CR14","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/0022-247X(83)90178-6","volume":"93","author":"J Lightbourne","year":"1983","unstructured":"Lightbourne, J., Rankin, S.: A partial functional differential equation of Sobolev type. J. Math. Anal. Appl. 93, 328\u2013337 (1983)","journal-title":"J. Math. Anal. Appl."},{"key":"2059_CR15","doi-asserted-by":"publisher","first-page":"3183","DOI":"10.1016\/j.camwa.2017.08.024","volume":"74","author":"Z Liu","year":"2017","unstructured":"Liu, Z., Mig\u00f3rski, S., Zeng, B.: Optimal feedback control and controllability for hyperbolic evolution inclusions of Clarke\u2019s subdifferential type. Comput. Math. Appl. 74, 3183\u20133194 (2017)","journal-title":"Comput. Math. Appl."},{"key":"2059_CR16","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10957-017-1122-3","volume":"174","author":"S Liu","year":"2017","unstructured":"Liu, S., Wang, J.: Optimal controls of systems governed by semilinear fractional differential equations with not instantaneous impulses. J. Optim. Theory Appl. 174, 455\u2013473 (2017)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"2059_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1615\/CritRevBiomedEng.v32.10","volume":"32","author":"RL Margin","year":"2004","unstructured":"Margin, R.L.: Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 32(1), 1\u2013104 (2004)","journal-title":"Crit. Rev. Biomed. Eng."},{"issue":"2","key":"2059_CR18","first-page":"205","volume":"62","author":"NI Mahmudov","year":"2014","unstructured":"Mahmudov, N.I.: Existence and approximate controllability of Sobolev type fractional stochastic evolution equations. Bull. Pol. Acad. Sci. Math. 62(2), 205\u2013215 (2014)","journal-title":"Bull. Pol. Acad. Sci. Math."},{"issue":"9","key":"2059_CR19","doi-asserted-by":"publisher","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(9), 1461\u20131477 (1996)","journal-title":"Chaos Solitons Fractals"},{"key":"2059_CR20","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0378-4371(99)00503-8","volume":"278","author":"R Metzler","year":"2000","unstructured":"Metzler, R., Klafter, I.: Boundary value problems for fractional diffusion equations. Phys. A 278, 107\u2013125 (2000)","journal-title":"Phys. A"},{"key":"2059_CR21","unstructured":"Michalski, M.W.: Derivatives of Noninteger Order and their Applications. Ph.D. Thesis, Polska Akademia Nauk (1993)"},{"key":"2059_CR22","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1016\/j.camwa.2011.04.044","volume":"62","author":"GM Mophoua","year":"2011","unstructured":"Mophoua, G.M., N\u2019Gu\u00e9r\u00e9kata, G.M.: Optimal control of a fractional diffusion equation with state constraints. Comput. Math. Appl. 62, 1413\u20131426 (2011)","journal-title":"Comput. Math. Appl."},{"key":"2059_CR23","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.chaos.2018.11.025","volume":"118","author":"L Peng","year":"2019","unstructured":"Peng, L., Zhou, Y., Debbouche, A.: Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces. Chaos Solitons Fractals 118, 234\u2013241 (2019)","journal-title":"Chaos Solitons Fractals"},{"key":"2059_CR24","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)"},{"key":"2059_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511666223","volume-title":"Stochastic Equations in Infinite Dimensions","author":"GD Prato","year":"1992","unstructured":"Prato, G.D., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (1992)"},{"issue":"1\u20132","key":"2059_CR26","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s11071-010-9697-3","volume":"62","author":"MR Rapai\u0107","year":"2010","unstructured":"Rapai\u0107, M.R., Jeli\u010di\u0107, Z.D.: Optimal control of a class of fractional heat diffusion systems. Nonlinear Dyn. 62(1\u20132), 39\u201351 (2010)","journal-title":"Nonlinear Dyn."},{"key":"2059_CR27","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.spl.2015.10.019","volume":"109","author":"P Revathi","year":"2016","unstructured":"Revathi, P., Sakthivel, R., Ren, Y.: Stochastic functional differential equations of Sobolev-type with infinite delay. Stat. Probab. Lett. 109, 68\u201377 (2016)","journal-title":"Stat. Probab. Lett."},{"key":"2059_CR28","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1063\/1.528578","volume":"30","author":"WR Schneider","year":"1989","unstructured":"Schneider, W.R., Wyss, W.: Fractional diffusion and wave equations. J. Math. Phys. 30, 134\u2013144 (1989)","journal-title":"J. Math. Phys."},{"key":"2059_CR29","doi-asserted-by":"publisher","first-page":"1427","DOI":"10.1016\/j.camwa.2011.02.040","volume":"62","author":"JR Wang","year":"2011","unstructured":"Wang, J.R., 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."},{"issue":"3","key":"2059_CR30","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1007\/s12555-016-0213-5","volume":"15","author":"Z Yan","year":"2017","unstructured":"Yan, Z., Jia, X.: Optimal controls of fractional impulsive partial neutral stochastic integro-differential systems with infinite delay in Hilbert spaces. Int. J. Control Autom. 15(3), 1051\u20131068 (2017)","journal-title":"Int. J. Control Autom."},{"key":"2059_CR31","doi-asserted-by":"publisher","first-page":"1581","DOI":"10.1007\/s40840-016-0415-2","volume":"41","author":"Z Yan","year":"2018","unstructured":"Yan, Z., Jia, X.: Optimal controls for fractional stochastic functional differential equations of order $$\\alpha \\in (1,2]$$. Bull. Malays. Math. Sci. Soc. 41, 1581\u20131606 (2018)","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"2059_CR32","doi-asserted-by":"publisher","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":"2059_CR33","doi-asserted-by":"publisher","first-page":"6775","DOI":"10.1002\/mma.5781","volume":"42","author":"Y Zhou","year":"2019","unstructured":"Zhou, Y., He, J.W., Ahmad, B., Tuan, N.H.: Existence and regularity results of a backward problem for fractional diffusion equations. Math. Meth. Appl. Sci. 42, 6775\u20136790 (2019)","journal-title":"Math. Meth. Appl. Sci."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02059-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02059-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02059-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T02:18:17Z","timestamp":1664417897000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02059-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,25]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["2059"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02059-2","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2022,6,25]]},"assertion":[{"value":"2 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}