{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T14:09:24Z","timestamp":1725977364843},"publisher-location":"Cham","reference-count":45,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319756462"},{"type":"electronic","value":"9783319756479"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"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":[[2018]]},"DOI":"10.1007\/978-3-319-75647-9_41","type":"book-chapter","created":{"date-parts":[[2018,5,8]],"date-time":"2018-05-08T18:48:41Z","timestamp":1525805321000},"page":"525-541","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Fuzzy Henstock\u2013Kurzweil Delta Integral on Time Scales"],"prefix":"10.1007","author":[{"given":"Dafang","family":"Zhao","sequence":"first","affiliation":[]},{"given":"Guoju","family":"Ye","sequence":"additional","affiliation":[]},{"given":"Wei","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,5,8]]},"reference":[{"key":"41_CR1","first-page":"77","volume":"16","author":"S Avsec","year":"2006","unstructured":"Avsec, S., Bannish, B., Johnson, B., Meckler, S.: The Henstock-Kurzweil delta integral on unbounded time scales. PanAmer. Math. J. 16, 77\u201398 (2006)","journal-title":"PanAmer. Math. J."},{"key":"41_CR2","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/978-3-319-32857-7_8","volume-title":"Differential and Difference Equations with Applications","author":"Benaoumeur Bayour","year":"2016","unstructured":"Bayour, B., Torres, D.F.M.: Complex-valued fractional derivatives on time scales. In: Differential and Difference Equations with Applications. Springer Proceedings in Mathematics and Statistics, vol. 164. pp. 79\u201387. Springer, Cham (2016)"},{"key":"41_CR3","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.sigpro.2014.05.026","volume":"107","author":"N Benkhettou","year":"2015","unstructured":"Benkhettou, N., Brito da Cruz, A.M.C., Torres, D.F.M.: A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration. Signal Process. 107, 230\u2013237 (2015)","journal-title":"Signal Process."},{"key":"41_CR4","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/mma.3475","volume":"39","author":"N Benkhettou","year":"2016","unstructured":"Benkhettou, N., Brito da Cruz, A.M.C., Torres, D.F.M.: Nonsymmetric and symmetric fractional calculus on arbitrary nonempty closed sets. Math. Methods Appl. Sci. 39, 261\u2013279 (2016)","journal-title":"Math. Methods Appl. Sci."},{"key":"41_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0201-1","volume-title":"Dynamic equations on time scales: an introduction with applications","author":"M Bohner","year":"2001","unstructured":"Bohner, M., Peterson, A.: Dynamic equations on time scales: an introduction with applications. Birkh\u00e4user, Boston, MA (2001)"},{"key":"41_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8230-9","volume-title":"Advances in dynamic equations on time scales","author":"M Bohner","year":"2003","unstructured":"Bohner, M., Peterson, A.: Advances in dynamic equations on time scales. Birkh\u00e4user, Boston, MA (2003)"},{"key":"41_CR7","doi-asserted-by":"crossref","first-page":"211","DOI":"10.21136\/MB.2006.134086","volume":"131","author":"B Bongiorno","year":"2006","unstructured":"Bongiorno, B., Piazza, L.D., Musia\u0142, K.: Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions. Math. Bohemica 131, 211\u2013223 (2006)","journal-title":"Math. Bohemica"},{"key":"41_CR8","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.fss.2011.12.006","volume":"200","author":"B Bongiorno","year":"2012","unstructured":"Bongiorno, B., Di Piazza, L., Musia\u0142, K.: A decomposition theorem for the fuzzy Henstock integral. Fuzzy Sets Syst. 200, 36\u201347 (2012)","journal-title":"Fuzzy Sets Syst."},{"issue":"4","key":"41_CR9","doi-asserted-by":"publisher","first-page":"1453","DOI":"10.1007\/s40840-014-0096-7","volume":"38","author":"AMC Brito da Cruz","year":"2015","unstructured":"Brito da Cruz, A.M.C., Martins, N., Torres, D.F.M.: The diamond integral on time scales. Bull. Malays. Math. Sci. Soc. 38(4), 1453\u20131462 (2015)","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"41_CR10","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1080\/10236190500272830","volume":"11","author":"A Cabada","year":"2005","unstructured":"Cabada, A., Vivero, D.R.: Criterions for absolute continuity on time scales. J. Differ. Equ. Appl. 11, 1013\u20131028 (2005)","journal-title":"J. Differ. Equ. Appl."},{"key":"41_CR11","first-page":"94","volume":"11","author":"M Cicho\u0144","year":"2011","unstructured":"Cicho\u0144, M.: On integrals of vector-valued functions on time scales. Commun. Math. Anal. 11, 94\u2013110 (2011)","journal-title":"Commun. Math. Anal."},{"key":"41_CR12","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s00605-013-0594-y","volume":"173","author":"L Piazza Di","year":"2014","unstructured":"Di Piazza, L., Musia\u0142, K.: Relations among Henstock McShane and Pettis integrals for multifunctions with compact convex values. Monatsh Math. 173, 459\u2013470 (2014)","journal-title":"Monatsh Math."},{"key":"41_CR13","first-page":"928","volume":"20","author":"KF Duan","year":"2016","unstructured":"Duan, K.F.: The Henstock-Stieltjes integral for fuzzy-number-valued functions on a infinite interval. J. Comput. Anal. Appl. 20, 928\u2013937 (2016)","journal-title":"J. Comput. Anal. Appl."},{"key":"41_CR14","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/s00500-014-1252-6","volume":"19","author":"OS Fard","year":"2015","unstructured":"Fard, O.S., Bidgoli, T.A.: Calculus of fuzzy functions on time scales (I). Soft. Comput. 19, 293\u2013305 (2015)","journal-title":"Soft. Comput."},{"key":"41_CR15","doi-asserted-by":"publisher","first-page":"152","DOI":"10.2298\/AADM160311004F","volume":"10","author":"OS Fard","year":"2016","unstructured":"Fard, O.S., Torres, D.F.M., Zadeh, M.R.: A Hukuhara approach to the study of hybrid fuzzy systems on time scales. Appl. Anal. Discret. Math. 10, 152\u2013167 (2016)","journal-title":"Appl. Anal. Discret. Math."},{"key":"41_CR16","doi-asserted-by":"publisher","first-page":"3816","DOI":"10.1016\/j.jde.2011.11.005","volume":"252","author":"M Federson","year":"2012","unstructured":"Federson, M., Mesquita, J.G., Slav\u00edk, A.: Measure functional differential equations and functional dynamic equations on time scales. J. Differ. Equ. 252, 3816\u20133847 (2012)","journal-title":"J. Differ. Equ."},{"key":"41_CR17","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/0165-0114(86)90026-6","volume":"18","author":"R Goetschel","year":"1986","unstructured":"Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18, 31\u201343 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR18","first-page":"55","volume":"27","author":"ZT Gong","year":"2003","unstructured":"Gong, Z.T.: The convergence theorems of the McShane interal of fuzzy-valued functions. Southeast Asian Bull. Math. 27, 55\u201362 (2003)","journal-title":"Southeast Asian Bull. Math."},{"key":"41_CR19","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1016\/j.fss.2008.10.013","volume":"160","author":"ZT Gong","year":"2009","unstructured":"Gong, Z.T., Shao, Y.B.: The controlled convergence theorems for the strong Henstock integrals of fuzzy-number-valued functions. Fuzzy Sets Syst. 160, 1528\u20131546 (2009)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR20","doi-asserted-by":"crossref","unstructured":"Gordon, R.A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics, vol. 4. American Mathematical Society, Providence, RI (1994)","DOI":"10.1090\/gsm\/004"},{"key":"41_CR21","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0022-247X(03)00361-5","volume":"285","author":"GSh Guseinov","year":"2003","unstructured":"Guseinov, GSh: Integration on time scales. J. Math. Anal. Appl. 285, 107\u2013127 (2003)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR22","first-page":"830","volume":"19","author":"ME Hamid","year":"2015","unstructured":"Hamid, M.E., Gong, Z.T.: The characterizations of McShane integral and Henstock integrals for fuzzy-number-valued functions with a small Riemann sum on a small set. J. Comput. Anal. Appl. 19, 830\u2013836 (2015)","journal-title":"J. Comput. Anal. Appl."},{"key":"41_CR23","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1112\/plms\/s3-11.1.402","volume":"11","author":"R Henstock","year":"1961","unstructured":"Henstock, R.: Definitions of Riemann type of variational integral. Proc. Lond. Math. Soc. 11, 402\u2013418 (1961)","journal-title":"Proc. Lond. Math. Soc."},{"key":"41_CR24","unstructured":"Hilger, S.: E$$\\imath $$n Ma\u00dfkettenkalk\u00fcl m$$\\imath $$t Anwendung auf Zentrumsmann$$\\imath $$gfalt$$\\imath $$gke$$\\imath $$ten, Ph.D. Thesis, Universt\u00e4t W\u00fcrzburg (1988)"},{"key":"41_CR25","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/0165-0114(87)90029-7","volume":"24","author":"O Kaleva","year":"1987","unstructured":"Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24, 301\u2013317 (1987)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR26","doi-asserted-by":"crossref","first-page":"418","DOI":"10.21136\/CMJ.1957.100258","volume":"7","author":"J Kurzweil","year":"1957","unstructured":"Kurzweil, J.: Generalized ordinary differential equations and continuous dependence on a parameter. Czech. Math. J. 7, 418\u2013446 (1957)","journal-title":"Czech. Math. J."},{"key":"41_CR27","doi-asserted-by":"crossref","unstructured":"Lee, T.Y.: Henstock-Kurzweil Integration on Euclidean Spaces. Series in Real Analysis, vol. 12. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2011)","DOI":"10.1142\/7933"},{"key":"41_CR28","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1016\/j.jmaa.2013.10.010","volume":"411","author":"GA Monteiro","year":"2014","unstructured":"Monteiro, G.A., Slav\u00edk, A.: Generalized elementary functions. J. Math. Anal. Appl. 411, 838\u2013852 (2014)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR29","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1016\/j.jmaa.2016.06.035","volume":"444","author":"GA Monteiro","year":"2016","unstructured":"Monteiro, G.A., Slav\u00edk, A.: Extremal solutions of measure differential equations. J. Math. Anal. Appl. 444, 568\u2013597 (2016)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR30","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.fss.2014.03.012","volume":"259","author":"K Musia\u0142","year":"2015","unstructured":"Musia\u0142, K.: A decomposition theorem for Banach space valued fuzzy Henstock integral. Fuzzy Sets Syst. 259, 21\u201328 (2015)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR31","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/j.cnsns.2016.03.010","volume":"39","author":"MD Ortigueira","year":"2016","unstructured":"Ortigueira, M.D., Torres, D.F.M., Trujillo, J.J.: Exponentials and Laplace transforms on nonuniform time scales. Commun. Nonlinear Sci. Numer. Simul. 39, 252\u2013270 (2016)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"41_CR32","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.jmaa.2005.10.025","volume":"323","author":"A Peterson","year":"2006","unstructured":"Peterson, A., Thompson, B.: Henstock-Kurzweil delta and nabla integrals. J. Math. Anal. Appl. 323, 162\u2013178 (2006)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR33","doi-asserted-by":"publisher","first-page":"1347","DOI":"10.2478\/s12175-013-0175-5","volume":"63","author":"BR Satco","year":"2013","unstructured":"Satco, B.R., Turcu, C.O.: Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on time scales. Math. Slovaca 63, 1347\u20131360 (2013)","journal-title":"Math. Slovaca"},{"key":"41_CR34","doi-asserted-by":"crossref","unstructured":"Schwabik, \u0160., Ye, G.J.: Topics in Banach Space Integration. Series in Real Analysis, vol. 10. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2005)","DOI":"10.1142\/9789812703286"},{"key":"41_CR35","doi-asserted-by":"crossref","unstructured":"Shao, Y.B., Zhang, H.H.: The strong fuzzy Henstock integrals and discontinuous fuzzy differential equations. J. Appl. Math. Art. ID 419701, 8 (2013)","DOI":"10.1155\/2013\/419701"},{"key":"41_CR36","first-page":"148","volume":"14","author":"YB Shao","year":"2014","unstructured":"Shao, Y.B., Zhang, H.H.: Existence of the solution for discontinuous fuzzy integro-differential equations and strong fuzzy Henstock integrals. Nonlinear Dyn. Syst. Theory 14, 148\u2013161 (2014)","journal-title":"Nonlinear Dyn. Syst. Theory"},{"key":"41_CR37","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.jmaa.2013.01.027","volume":"402","author":"A Slav\u00edk","year":"2013","unstructured":"Slav\u00edk, A.: Generalized differential equations: differentiability of solutions with respect to initial conditions and parameters. J. Math. Anal. Appl. 402, 261\u2013274 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR38","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1016\/j.jmaa.2014.11.037","volume":"424","author":"A Slav\u00edk","year":"2015","unstructured":"Slav\u00edk, A.: Kurzweil and McShane product integration in Banach algebras. J. Math. Anal. Appl. 424, 748\u2013773 (2015)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR39","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1016\/j.jde.2015.02.013","volume":"259","author":"A Slav\u00edk","year":"2015","unstructured":"Slav\u00edk, A.: Well-posedness results for abstract generalized differential equations and measure functional differential equations. J. Differ. Equ. 259, 666\u2013707 (2015)","journal-title":"J. Differ. Equ."},{"key":"41_CR40","first-page":"1","volume":"18","author":"BS Thompson","year":"2008","unstructured":"Thompson, B.S.: Henstock-Kurzweil integrals on time scales. Panamer. Math. J. 18, 1\u201319 (2008)","journal-title":"Panamer. Math. J."},{"key":"41_CR41","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/S0165-0114(98)00277-2","volume":"115","author":"CX Wu","year":"2000","unstructured":"Wu, C.X., Gong, Z.T.: On Henstock integrals of interval-valued functions and fuzzy-valued functions. Fuzzy Sets Syst. 115, 377\u2013391 (2000)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR42","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/S0165-0114(99)00057-3","volume":"120","author":"CX Wu","year":"2001","unstructured":"Wu, C.X., Gong, Z.T.: On Henstock integral of fuzzy-number-valued functions(I). Fuzzy Sets Syst. 120, 523\u2013532 (2001)","journal-title":"Fuzzy Sets Syst."},{"key":"41_CR43","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1016\/j.jmaa.2006.08.020","volume":"330","author":"GJ Ye","year":"2007","unstructured":"Ye, G.J.: On Henstock-Kurzweil and McShane integrals of Banach space-valued functions. J. Math. Anal. Appl. 330, 753\u2013765 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"41_CR44","doi-asserted-by":"publisher","first-page":"2487","DOI":"10.22436\/jnsa.010.05.18","volume":"10","author":"XX You","year":"2017","unstructured":"You, X.X., Zhao, D.F., Torres, D.F.M.: On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales. J. Nonlinear Sci. Appl. 10, 2487\u20132500 (2017)","journal-title":"J. Nonlinear Sci. Appl."},{"key":"41_CR45","first-page":"177","volume":"19","author":"DF Zhao","year":"2006","unstructured":"Zhao, D.F., Ye, G.J.: On ap-Henstock-Stieltjes integral. J. Chungcheong Math. Soc. 19, 177\u2013187 (2006)","journal-title":"J. Chungcheong Math. Soc."}],"container-title":["Springer Proceedings in Mathematics & Statistics","Differential and Difference Equations with Applications"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-75647-9_41","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T18:58:26Z","timestamp":1604257106000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-75647-9_41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319756462","9783319756479"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-75647-9_41","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2018]]}}}