{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:16:37Z","timestamp":1783667797218,"version":"3.55.0"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117894","type":"journal-article","created":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T01:01:32Z","timestamp":1781312492000},"page":"117894","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Solving optimal control problems using the variational differential quadrature method"],"prefix":"10.1016","volume":"489","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1014-7079","authenticated-orcid":false,"given":"M.","family":"Faraji Oskouie","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Ansari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Rouhi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117894_bib0001","series-title":"Optimal Control: An Introduction to the Theory and Its Applications","author":"Athans","year":"2007"},{"key":"10.1016\/j.cam.2026.117894_bib0002","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/81.974886","article-title":"Discretized quadratic optimal control for continuous-time two-dimensional systems","volume":"49","author":"Tsai","year":"2002","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"10.1016\/j.cam.2026.117894_bib0003","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/S0016-0032(02)00028-5","article-title":"Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials","volume":"339","author":"Jaddu","year":"2002","journal-title":"J. Frankl. Inst."},{"key":"10.1016\/j.cam.2026.117894_bib0004","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1007\/s00231-002-0314-y","article-title":"A three-dimensional optimal control problem in determining the boundary control heat fluxes","volume":"39","author":"Huang","year":"2003","journal-title":"Heat Mass Transf."},{"key":"10.1016\/j.cam.2026.117894_bib0005","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1016\/j.matcom.2008.02.014","article-title":"Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time","volume":"79","author":"Gerdts","year":"2008","journal-title":"Math. Comput. Simul."},{"key":"10.1016\/j.cam.2026.117894_bib0006","series-title":"International Series of Numerical Mathematics","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/978-3-0348-0133-1_24","article-title":"Numerical analysis of state-constrained optimal control problems for PDEs","volume":"160","author":"Neitzel","year":"2011"},{"key":"10.1016\/j.cam.2026.117894_bib0007","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1051\/cocv\/2010025","article-title":"Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations","volume":"17","author":"Casas","year":"2011","journal-title":"ESAIM COCV"},{"key":"10.1016\/j.cam.2026.117894_bib0008","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.actaastro.2011.10.004","article-title":"Solution of nonlinear optimal control problems by the interpolating scaling functions","volume":"72","author":"Foroozandeh","year":"2012","journal-title":"Acta Astronaut."},{"key":"10.1016\/j.cam.2026.117894_bib0009","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1051\/m2an\/2012037","article-title":"A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD","volume":"47","author":"Kammann","year":"2013","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117894_bib0010","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1002\/oca.2191","article-title":"Numerical solution of a class of two-dimensional quadratic optimal control problems by using Ritz method","volume":"37","author":"Mamehrashi","year":"2015","journal-title":"Optim. Control Appl. Meth."},{"key":"10.1016\/j.cam.2026.117894_bib0011","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1080\/00207179.2016.1178807","article-title":"A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation","volume":"90","author":"Mamehrashi","year":"2017","journal-title":"Int. J. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0012","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1016\/j.camwa.2009.08.006","article-title":"An approximate method for numerically solving fractional order optimal control problems of general form","volume":"59","author":"Tricaud","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117894_bib0013","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1016\/j.camwa.2011.03.064","article-title":"Generalized Euler\u2013Lagrange equations for fractional variational problems with free boundary conditions","volume":"62","author":"Yousefi","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117894_bib0014","doi-asserted-by":"crossref","first-page":"2059","DOI":"10.1177\/1077546311399950","article-title":"The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems","volume":"17","author":"Yousefi","year":"2011","journal-title":"J. Vib. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0015","doi-asserted-by":"crossref","first-page":"2523","DOI":"10.1177\/1077546312458308","article-title":"Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices","volume":"19","author":"Alipour","year":"2012","journal-title":"J. Vib. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0016","doi-asserted-by":"crossref","first-page":"2389","DOI":"10.1002\/asjc.1109","article-title":"An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index","volume":"17","author":"Bhrawy","year":"2015","journal-title":"Asian J. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0017","doi-asserted-by":"crossref","first-page":"3889","DOI":"10.1177\/1077546314567181","article-title":"A numerical solution for fractional optimal control problems via Bernoulli polynomials","volume":"22","author":"Keshavarz","year":"2016","journal-title":"J. Vib. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0018","article-title":"A numerical method for solving fractional optimal control problems using Ritz method","volume":"11","author":"Nemati","year":"2016","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117894_bib0019","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1007\/s10957-016-0912-3","article-title":"A generalization of ritz-variational method for solving a class of fractional optimization problems","volume":"174","author":"Lotfi","year":"2017","journal-title":"J. Optim. Theor. Appl."},{"key":"10.1016\/j.cam.2026.117894_bib0020","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10957-017-1106-3","article-title":"A combination of variational and penalty methods for solving a class of fractional optimal control problems","volume":"174","author":"Lotfi","year":"2017","journal-title":"J. Optim. Theor. Appl."},{"key":"10.1016\/j.cam.2026.117894_bib0021","doi-asserted-by":"crossref","first-page":"5466","DOI":"10.1002\/mma.5090","article-title":"B-spline spectral method for constrained fractional optimal control problems","volume":"41","author":"Ejlali","year":"2018","journal-title":"Math. Meth. Appl. Sci."},{"issue":"14","key":"10.1016\/j.cam.2026.117894_bib0022","first-page":"3909","article-title":"Fractional-order Lagrange polynomials: an application for solving delay fractional optimal control problems","volume":"41","author":"Sabermahani","year":"2019","journal-title":"Trans. Inst. Meas. Control"},{"key":"10.1016\/j.cam.2026.117894_bib0023","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1007\/s00366-019-00730-3","article-title":"Fractional-order Fibonacci-hybrid functions approach for solving fractional delay differential equations","volume":"36","author":"Sabermahani","year":"2020","journal-title":"Eng. with Comput."},{"key":"10.1016\/j.cam.2026.117894_bib0024","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.apm.2017.02.052","article-title":"Variational differential quadrature: a technique to simplify numerical analysis of structures","volume":"49","author":"Faghih Shojaei","year":"2017","journal-title":"Appl. Math. Model."},{"key":"10.1016\/j.cam.2026.117894_bib0025","doi-asserted-by":"crossref","DOI":"10.1093\/imamci\/dnw009","article-title":"A numerical scheme for solving two-dimensional fractional optimal control problems by the Ritz method combined with fractional operational matrix","author":"Nemati","year":"2016","journal-title":"IMA J. Math. Control Inform."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005364?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005364?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:47:41Z","timestamp":1783666061000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":25,"alternative-id":["S0377042726005364"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117894","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Solving optimal control problems using the variational differential quadrature method","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117894","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117894"}}