{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:09:27Z","timestamp":1759032567857},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2016,1,2]],"date-time":"2016-01-02T00:00:00Z","timestamp":1451692800000},"content-version":"tdm","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":[[2017,5]]},"DOI":"10.1007\/s00500-015-1980-2","type":"journal-article","created":{"date-parts":[[2016,1,2]],"date-time":"2016-01-02T07:34:53Z","timestamp":1451720093000},"page":"2777-2784","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Interval Abel integral equation"],"prefix":"10.1007","volume":"21","author":[{"given":"Vasile","family":"Lupulescu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ngo","family":"Van Hoa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,2]]},"reference":[{"key":"1980_CR1","doi-asserted-by":"publisher","first-page":"572","DOI":"10.2478\/s13540-012-0040-1","volume":"15","author":"RP Agarwal","year":"2012","unstructured":"Agarwal RP, Arshad S, O\u2019Regan D, Lupulescu V (2012) Fuzzy fractional integral equations under compactness type condition. Fract Calc Appl Anal 15:572\u2013590","journal-title":"Fract Calc Appl Anal"},{"key":"1980_CR2","doi-asserted-by":"publisher","first-page":"2859","DOI":"10.1016\/j.na.2009.11.029","volume":"72","author":"RP Agarwal","year":"2010","unstructured":"Agarwal RP, Lakshmikantham V, Nieto JJ (2010) On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal TMA 72:2859\u20132862","journal-title":"Nonlinear Anal TMA"},{"key":"1980_CR3","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00500-011-0743-y","volume":"16","author":"T Allahviranloo","year":"2012","unstructured":"Allahviranloo T, Salahshour S, Abbasbandy S (2012) Explicit solutions of fractional differential equations with uncertainty. Soft Comput 16:297\u2013302","journal-title":"Soft Comput"},{"key":"1980_CR4","doi-asserted-by":"publisher","first-page":"3685","DOI":"10.1016\/j.na.2011.02.048","volume":"74","author":"S Arshad","year":"2011","unstructured":"Arshad S, Lupulescu V (2011) On the fractional differential equations with uncertainty. Nonlinear Anal TMA 74:3685\u20133693","journal-title":"Nonlinear Anal TMA"},{"key":"1980_CR5","first-page":"1","volume":"34","author":"S Arshad","year":"2011","unstructured":"Arshad S, Lupulescu V (2011) Fractional differential equation with fuzzy initial condition. Electron J Differ Equ 34:1\u20138","journal-title":"Electron J Differ Equ"},{"key":"1980_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-247X(65)90049-1","volume":"12","author":"RJ Aumann","year":"1965","unstructured":"Aumann RJ (1965) Integrals of set-valued functions. J Math Anal Appl 12:1\u201312","journal-title":"J Math Anal Appl"},{"key":"1980_CR7","doi-asserted-by":"publisher","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":"1980_CR8","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.fss.2012.10.003","volume":"230","author":"B Bede","year":"2013","unstructured":"Bede B, Stefanini L (2013) Generalized differentiability of fuzzy-valued functions. Fuzzy Sets Syst 230:119\u2013141","journal-title":"Fuzzy Sets Syst"},{"key":"1980_CR9","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.1016\/j.ins.2011.01.023","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. Inf Sci 181:2177\u20132188","journal-title":"Inf Sci"},{"key":"1980_CR10","doi-asserted-by":"publisher","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"},{"key":"1980_CR11","unstructured":"Debreu G (1966) Integration of correspondences. In: Proceedings of fifth Berkeley symposium on mathematics statistical and probability, Vol II, part I, pp 351\u2013372"},{"key":"1980_CR12","volume-title":"Abel integral equations: analysis and applications","author":"R Gorenflo","year":"1977","unstructured":"Gorenflo R, Vessella S (1977) Abel integral equations: analysis and applications. Springer, Berlin"},{"key":"1980_CR13","doi-asserted-by":"publisher","unstructured":"Hoa NV (2015a) The initial value problem for interval-valued second-order differential equations under generalized H-differentiability. Inf Sci 311:119\u2013148","DOI":"10.1016\/j.ins.2015.03.029"},{"key":"1980_CR14","doi-asserted-by":"publisher","unstructured":"Hoa NV (2015b) Fuzzy fractional functional integral and differential equations. Fuzzy Sets Syst 280:58\u201390","DOI":"10.1016\/j.fss.2015.01.009"},{"key":"1980_CR15","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0047-259X(77)90037-9","volume":"7","author":"F Hiai","year":"1977","unstructured":"Hiai F, Umegaki H (1977) Integrals, conditional expectations and martingales of multivalued functions. J Multivar Anal 7:149\u2013182","journal-title":"J Multivar Anal"},{"key":"1980_CR16","unstructured":"Hukuhara M (1967) Int\u00e9gration des applications mesurables dont la valeur est un compact convex. Funkcial. Ekvac. 10: 205\u2013229"},{"key":"1980_CR17","doi-asserted-by":"publisher","unstructured":"Lupulescu V (2013) Hukuhara differentiability of interval-valued functions and interval differential equations on time scales. Inf Sci 248:50\u201367","DOI":"10.1016\/j.ins.2013.06.004"},{"key":"1980_CR18","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.fss.2014.04.005","volume":"265","author":"V Lupulescu","year":"2015","unstructured":"Lupulescu V (2015) Fractional calculus for interval-valued functions. Fuzzy Sets Syst 265:63\u201385","journal-title":"Fuzzy Sets Syst"},{"key":"1980_CR19","doi-asserted-by":"publisher","first-page":"2118","DOI":"10.1016\/j.aml.2011.06.011","volume":"24","author":"MT Malinowski","year":"2011","unstructured":"Malinowski MT (2011) Interval differential equations with a second type Hukuhara derivative. Appl Math Lett 24:2118\u20132123","journal-title":"Appl Math Lett"},{"key":"1980_CR20","doi-asserted-by":"publisher","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. Inform Sci 213:94\u2013105","journal-title":"Inform Sci"},{"key":"1980_CR21","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1016\/j.nonrwa.2011.08.022","volume":"13","author":"MT Malinowski","year":"2012","unstructured":"Malinowski MT (2012) Random fuzzy differential equations under generalized Lipschitz condition. Nonlinear Anal Real World Appl 13:860\u2013881","journal-title":"Nonlinear Anal Real World Appl"},{"key":"1980_CR22","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.amc.2012.06.019","volume":"219","author":"MT Malinowski","year":"2012","unstructured":"Malinowski MT (2012) On set differential equations in Banach spaces\u2014a second type Hukuhara differentiability approach. Appl Math Comput 219:289\u2013305","journal-title":"Appl Math Comput"},{"key":"1980_CR23","doi-asserted-by":"publisher","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 variables. Computing 22:325\u2013337","journal-title":"Computing"},{"key":"1980_CR24","doi-asserted-by":"publisher","unstructured":"Moore RE (1979) Methods and applications of interval analysis. SIAM studies in applied mathematics, Philadelphia","DOI":"10.1137\/1.9781611970906"},{"key":"1980_CR25","first-page":"1","volume":"112","author":"S Salahshour","year":"2012","unstructured":"Salahshour S, Allahviranloo T, Abbasbandy S, Baleanu D (2012) Existence and uniqueness results for fractional differential equations with uncertainty. Adv Differ Equ 112:1\u201317","journal-title":"Adv Differ Equ"},{"key":"1980_CR26","volume-title":"Fractional integrals and derivatives: theory and applications","author":"SG Samko","year":"1993","unstructured":"Samko SG, Kilbas AA, Marichev OI (1993) Fractional integrals and derivatives: theory and applications. Gordon and Breach Science Publishers, Switzerland"},{"key":"1980_CR27","doi-asserted-by":"publisher","unstructured":"Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 161:1564\u20131584","DOI":"10.1016\/j.fss.2009.06.009"},{"key":"1980_CR28","doi-asserted-by":"publisher","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 71:1311\u20131328","journal-title":"Nonlinear Anal"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1980-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-015-1980-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1980-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1980-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T15:03:20Z","timestamp":1718291000000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-015-1980-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,2]]},"references-count":28,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["1980"],"URL":"https:\/\/doi.org\/10.1007\/s00500-015-1980-2","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,2]]}}}