{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:50:11Z","timestamp":1772290211554,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2017,9,6]],"date-time":"2017-09-06T00:00:00Z","timestamp":1504656000000},"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":["Soft Comput"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s00500-017-2818-x","type":"journal-article","created":{"date-parts":[[2017,9,6]],"date-time":"2017-09-06T03:40:54Z","timestamp":1504669254000},"page":"3817-3828","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Solving a nonhomogeneous linear system of interval differential equations"],"prefix":"10.1007","volume":"22","author":[{"given":"Nizami A.","family":"Gasilov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7747-5467","authenticated-orcid":false,"given":"\u015eahin","family":"Emrah Amrahov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,6]]},"reference":[{"key":"2818_CR1","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.fss.2015.12.002","volume":"295","author":"\u015eE Amrahov","year":"2016","unstructured":"Amrahov \u015eE, Khastan A, Gasilov N, Fatullayev AG (2016) Relationship between Bede-Gal differentiable set-valued functions and their associated support functions. Fuzzy Sets Syst 295:57\u201371","journal-title":"Fuzzy Sets Syst"},{"key":"2818_CR2","volume-title":"Set-valued analysis","author":"J-P Aubin","year":"1990","unstructured":"Aubin J-P, Frankowska H (1990) Set-valued analysis. Birkh\u00e4user, Boston"},{"issue":"1","key":"2818_CR3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11784-015-0236-1","volume":"17","author":"D Azzam-Laouir","year":"2015","unstructured":"Azzam-Laouir D, Boukrouk W (2015) Second-order set-valued differential equations with boundary conditions. J Fixed Point Theory Appl 17(1):99\u2013121","journal-title":"J Fixed Point Theory Appl"},{"key":"2818_CR4","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0022-247X(70)90078-8","volume":"29","author":"HT Banks","year":"1970","unstructured":"Banks HT, Jacobs MQ (1970) A differential calculus for multifunctions. J Math Anal Appl 29:246\u2013272","journal-title":"J Math Anal Appl"},{"key":"2818_CR5","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/j.fss.2004.08.001","volume":"151","author":"B Bede","year":"2005","unstructured":"Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581\u2013599","journal-title":"Fuzzy Sets Syst"},{"key":"2818_CR6","unstructured":"Bede B, Stefanini L (2009) Numerical solution of interval differential equations with generalized Hukuhara differentiability. In: Proceedings of the joint 2009 International fuzzy systems association world congress and 2009 European society of fuzzy logic and technology conference , pp 730\u2013735"},{"issue":"4","key":"2818_CR7","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/j.ijheatmasstransfer.2009.10.014","volume":"53","author":"B Blackwell","year":"2010","unstructured":"Blackwell B, Beck JV (2010) A technique for uncertainty analysis for inverse heat conduction problems. Int J Heat Mass Transf 53(4):753\u2013759","journal-title":"Int J Heat Mass Transf"},{"key":"2818_CR8","first-page":"199","volume":"169","author":"VI Blagodatskikh","year":"1986","unstructured":"Blagodatskikh VI, Filippov AF (1986) Differential inclusions and optimal control. Proc Steklov Inst Math 169:199\u2013259","journal-title":"Proc Steklov Inst Math"},{"issue":"1","key":"2818_CR9","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1006\/jmaa.1994.1017","volume":"181","author":"FG Boese","year":"1994","unstructured":"Boese FG (1994) Stability in a special class of retarded difference-differential equations with interval-valued parameters. J Math Anal Appl 181(1):227\u2013247","journal-title":"J Math Anal Appl"},{"issue":"1","key":"2818_CR10","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2140\/pjm.1970.33.43","volume":"33","author":"TF Bridgland","year":"1970","unstructured":"Bridgland TF (1970) Trajectory integrals of set-valued functions. Pac J Math 33(1):43\u201368","journal-title":"Pac J Math"},{"key":"2818_CR11","first-page":"2177","volume":"181","author":"Y Chalco-Cano","year":"2011","unstructured":"Chalco-Cano Y, Rom\u00e1n-Flores H, Jim\u00e9nez-Gamero MD (2011) Generalized derivative and $$\\pi $$ \u03c0 -derivative for set-valued functions. Fuzzy Sets Syst 181:2177\u20132188","journal-title":"Fuzzy Sets Syst"},{"key":"2818_CR12","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.fss.2012.12.004","volume":"219","author":"Y Chalco-Cano","year":"2013","unstructured":"Chalco-Cano Y, Rufi\u00e1n-Lizana A, Rom\u00e1n-Flores H, Jim\u00e9nez-Gamero MD (2013) Calculus for interval-valued functions using generalized Hukuhara derivative and applications. Fuzzy Sets Syst 219:49\u201367","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"2818_CR13","doi-asserted-by":"crossref","first-page":"765","DOI":"10.3934\/jimo.2012.8.765","volume":"8","author":"T Dabbous","year":"2012","unstructured":"Dabbous T (2012) Identification for systems governed by nonlinear interval differential equations. J Ind Manag Optim 8(3):765\u2013780","journal-title":"J Ind Manag Optim"},{"issue":"4","key":"2818_CR14","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.na.2005.01.004","volume":"61","author":"GN Galanis","year":"2005","unstructured":"Galanis GN, Bhaskar TG, Lakshmikantham V et al (2005) Set valued functions in Frechet spaces: continuity Hukuhara differentiability and applications to set differential equations. Nonlinear Anal Theory Methods Appl 61(4):559\u2013575","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"3","key":"2818_CR15","first-page":"484","volume":"5","author":"N Gasilov","year":"2011","unstructured":"Gasilov N, Amrahov \u015eE, Fatullayev AG (2011) A geometric approach to solve fuzzy linear systems of differential equations. Appl Math Inf Sci 5(3):484\u2013499","journal-title":"Appl Math Inf Sci"},{"key":"2818_CR16","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.fss.2013.08.008","volume":"257","author":"N Gasilov","year":"2014","unstructured":"Gasilov N, Amrahov \u015eE, Fatullayev AG (2014a) Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst 257:169\u2013183","journal-title":"Fuzzy Sets Syst"},{"key":"2818_CR17","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00500-013-1081-z","volume":"18","author":"NA Gasilov","year":"2014","unstructured":"Gasilov NA, Fatullayev AG, Amrahov \u015eE, Khastan A (2014b) A new approach to fuzzy initial value problem. Soft Comput 18:217\u2013225","journal-title":"Soft Comput"},{"key":"2818_CR18","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.ins.2015.05.002","volume":"317","author":"NA Gasilov","year":"2015","unstructured":"Gasilov NA, Amrahov \u015eE, Fatullayev AG, Hashimoglu IF (2015) Solution method for a boundary value problem with fuzzy forcing function. Inf Sci 317:349\u2013368","journal-title":"Inf Sci"},{"key":"2818_CR19","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ins.2015.03.029","volume":"311","author":"NV Hoa","year":"2015","unstructured":"Hoa NV (2015) The initial value problem for interval-valued second-order differential equations under generalized H-differentiability. Inf Sci 311:119\u2013148","journal-title":"Inf Sci"},{"key":"2818_CR20","doi-asserted-by":"crossref","unstructured":"Hoa NV, Phu ND, Tung TT et\u00a0al (2014) Interval-valued functional integro-differential equations. Adv Differ Equ, Article number: 177","DOI":"10.1186\/1687-1847-2014-177"},{"key":"2818_CR21","first-page":"205","volume":"10","author":"M Hukuhara","year":"1967","unstructured":"Hukuhara M (1967) Int\u00e9gration des applications mesurables dont la valeur est un compact convexe. Funkcial Ekvac 10:205\u2013223","journal-title":"Funkcial Ekvac"},{"key":"2818_CR22","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1142\/S0218488597000117","volume":"5","author":"E H\u00fcllermeier","year":"1997","unstructured":"H\u00fcllermeier E (1997) An approach to modeling and simulation of uncertain dynamical systems. Int J Uncertain Fuzziness Knowl Based Syst 5:117\u2013137","journal-title":"Int J Uncertain Fuzziness Knowl Based Syst"},{"issue":"10","key":"2818_CR23","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1007\/s11253-009-0150-z","volume":"60","author":"TA Komleva","year":"2008","unstructured":"Komleva TA, Plotnikov AV, Skripnik NV (2008) Differential equations with set-valued solutions. Ukr Math J 60(10):1540\u20131556","journal-title":"Ukr Math J"},{"issue":"1","key":"2818_CR24","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0096-3003(91)90108-Y","volume":"41","author":"V Lakshmikantham","year":"1991","unstructured":"Lakshmikantham V, Sun Y (1991) Applications of interval-analysis to minimal and maximal solutions of differential equations. Appl Math Comput 41(1):77\u201387","journal-title":"Appl Math Comput"},{"issue":"2","key":"2818_CR25","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0362-546X(03)00067-1","volume":"54","author":"V Lakshmikantham","year":"2003","unstructured":"Lakshmikantham V, Leela S, Vatsala AS (2003) Interconnection between set and fuzzy differential equations. Nonlinear Anal Theory Methods Appl 54(2):351\u2013360","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"2818_CR26","volume-title":"Theory of set differential equations in metric spaces","author":"V Lakshmikantham","year":"2006","unstructured":"Lakshmikantham V, Bhaskar TG, Devi JV (2006) Theory of set differential equations in metric spaces. Cambridge Scientific Publ, Cambridge"},{"key":"2818_CR27","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.ins.2013.06.004","volume":"248","author":"V Lupulescu","year":"2013","unstructured":"Lupulescu V (2013) Hukuhara differentiability of interval-valued functions and interval differential equations on time scales. Inf Sci 248:50\u201367","journal-title":"Inf Sci"},{"key":"2818_CR28","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.ins.2012.05.022","volume":"213","author":"MT Malinowski","year":"2012","unstructured":"Malinowski MT (2012) Interval Cauchy problem with a second type Hukuhara derivative. Inf Sci 213:94\u2013105","journal-title":"Inf Sci"},{"issue":"18","key":"2818_CR29","doi-asserted-by":"crossref","first-page":"9427","DOI":"10.1016\/j.amc.2012.03.027","volume":"218","author":"MT Malinowski","year":"2012","unstructured":"Malinowski MT (2012) Second type Hukuhara differentiable solutions to the delay set-valued differential equations. Appl Math Comput 218(18):9427\u20139437","journal-title":"Appl Math Comput"},{"key":"2818_CR30","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/978-3-319-10765-3_13","volume":"315","author":"MT Malinowski","year":"2015","unstructured":"Malinowski MT (2015) Fuzzy and set-valued stochastic differential equations with solutions of decreasing fuzziness. Adv Intell Syst Comput 315:105\u2013112","journal-title":"Adv Intell Syst Comput"},{"key":"2818_CR31","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02265313","volume":"22","author":"S Markov","year":"1979","unstructured":"Markov S (1979) Calculus for interval functions of a real variable. Computing 22:325\u2013337","journal-title":"Computing"},{"key":"2818_CR32","volume-title":"Interval analysis","author":"RE Moore","year":"1966","unstructured":"Moore RE (1966) Interval analysis. Prentice-Hall, Englewood Cliffs"},{"issue":"4","key":"2818_CR33","first-page":"632","volume":"19","author":"L-X Pan","year":"2015","unstructured":"Pan L-X (2015) The numerical solution for the interval-valued differential equations. J Comput Anal Appl 19(4):632\u2013641","journal-title":"J Comput Anal Appl"},{"key":"2818_CR34","doi-asserted-by":"crossref","unstructured":"Phu ND, An TV, Hoa NV et\u00a0al (2014) Interval-valued functional differential equations under dissipative conditions. Adv Differ Equ, Article number: 198","DOI":"10.1186\/1687-1847-2014-198"},{"issue":"8","key":"2818_CR35","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1023\/A:1010361206391","volume":"52","author":"AV Plotnikov","year":"2000","unstructured":"Plotnikov AV (2000) Differentiation of multivalued mappings. T-derivative. Ukr Math J 52(8):1282\u20131291","journal-title":"Ukr Math J"},{"issue":"10","key":"2818_CR36","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1007\/s11253-014-0875-1","volume":"65","author":"AV Plotnikov","year":"2014","unstructured":"Plotnikov AV, Skripnik NV (2014) Conditions for the existence of local solutions of set-valued differential equations with generalized derivative. Ukr Math J 65(10):1498\u20131513","journal-title":"Ukr Math J"},{"issue":"11","key":"2818_CR37","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1070\/SM2005v196n11ABEH003726","volume":"196","author":"NV Plotnikova","year":"2005","unstructured":"Plotnikova NV (2005) Systems of linear differential equations with $$\\pi $$ \u03c0 -derivative and linear differential inclusions. Sbornik Math 196(11):1677\u20131691","journal-title":"Sbornik Math"},{"issue":"6","key":"2818_CR38","doi-asserted-by":"crossref","first-page":"3495","DOI":"10.3233\/IFS-162096","volume":"30","author":"LT Quang","year":"2016","unstructured":"Quang LT, Hoa NV, Phu ND et al (2016) Existence of extremal solutions for interval-valued functional integro-differential equations. J Intell Fuzzy Syst 30(6):3495\u20133512","journal-title":"J Intell Fuzzy Syst"},{"issue":"2\u20133","key":"2818_CR39","first-page":"201","volume":"47","author":"S Sivasundaram","year":"1992","unstructured":"Sivasundaram S, Sun Y (1992) Application of interval analysis to impulsive differential equations. Appl Math Comput 47(2\u20133):201\u2013210","journal-title":"Appl Math Comput"},{"issue":"4","key":"2818_CR40","doi-asserted-by":"crossref","first-page":"116","DOI":"10.5923\/j.am.20120204.03","volume":"2","author":"N Skripnik","year":"2012","unstructured":"Skripnik N (2012) Interval-valued differential equations with generalized derivative. Appl Math 2(4):116\u2013120","journal-title":"Appl Math"},{"issue":"11","key":"2818_CR41","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1016\/j.fss.2009.06.009","volume":"161","author":"L Stefanini","year":"2010","unstructured":"Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 161(11):1564\u20131584","journal-title":"Fuzzy Sets Syst"},{"issue":"3\u20134","key":"2818_CR42","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","volume":"71","author":"L Stefanini","year":"2009","unstructured":"Stefanini L, Bede B (2009) Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal Theory Methods Appl 71(3\u20134):1311\u20131328","journal-title":"Nonlinear Anal Theory Methods Appl"},{"key":"2818_CR43","first-page":"1","volume":"45","author":"J Tao","year":"2016","unstructured":"Tao J, Zhang Z (2016) Properties of interval-valued function space under the gH-difference and their application to semi-linear interval differential equations. Adv Differ Equ 45:1\u201328","journal-title":"Adv Differ Equ"},{"issue":"5","key":"2818_CR44","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1002\/nme.4932","volume":"104","author":"C Wang","year":"2015","unstructured":"Wang C, Qiu Z, He Y (2015) Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters. Int J Numer Methods Eng 104(5):330\u2013346","journal-title":"Int J Numer Methods Eng"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-017-2818-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2818-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-017-2818-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T13:50:26Z","timestamp":1692971426000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-017-2818-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,6]]},"references-count":44,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["2818"],"URL":"https:\/\/doi.org\/10.1007\/s00500-017-2818-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,6]]}}}