{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T06:51:23Z","timestamp":1767423083805,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T00:00:00Z","timestamp":1638144000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T00:00:00Z","timestamp":1638144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"crossref","award":["2018\/10946-2"],"award-info":[{"award-number":["2018\/10946-2"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["306546\/2017-5"],"award-info":[{"award-number":["306546\/2017-5"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s40314-021-01695-0","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T03:02:40Z","timestamp":1638154960000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Solution to the Bessel differential equation with interactive fuzzy boundary conditions"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4660-5884","authenticated-orcid":false,"given":"Daniel Eduardo","family":"S\u00e1nchez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0965-0654","authenticated-orcid":false,"given":"Vin\u00edcius Francisco","family":"Wasques","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Estev\u00e3o","family":"Esmi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"La\u00e9cio Carvalho","family":"de Barros","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,29]]},"reference":[{"issue":"7","key":"1695_CR1","doi-asserted-by":"publisher","first-page":"075218","DOI":"10.1088\/1402-4896\/ab96e0","volume":"95","author":"M Al-Smadi","year":"2020","unstructured":"Al-Smadi M, Arqub OA, Momani S (2020) Numerical computations of coupled fractional resonant Schr\u00f6dinger equations arising in quantum mechanics under conformable fractional derivative sense. Phys Scr 95(7):075218","journal-title":"Phys Scr"},{"key":"1695_CR2","doi-asserted-by":"publisher","first-page":"110891","DOI":"10.1016\/j.chaos.2021.110891","volume":"146","author":"M Al-Smadi","year":"2021","unstructured":"Al-Smadi M, Arqub OA, Zeidan D (2021a) Fuzzy fractional differential equations under the Mittag\u2013Leffler kernel differential operator of the ABC approach: theorems and applications. Chaos Solit Fract 146:110891","journal-title":"Chaos Solit Fract"},{"key":"1695_CR3","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1051\/mmnp\/2021030","volume":"16","author":"M Al-Smadi","year":"2021","unstructured":"Al-Smadi M, Dutta H, Hasan S, Momani S (2021b) On numerical approximation of Atangana\u2013Baleanu\u2013Caputo fractional integro-differential equations under uncertainty in Hilbert Space. Math Model Nat Phenomena 16:41","journal-title":"Math Model Nat Phenomena"},{"key":"1695_CR4","volume-title":"Soft numerical computing in uncertain dynamic systems","author":"T Allahviranloo","year":"2020","unstructured":"Allahviranloo T, Pedrycz W (2020) Soft numerical computing in uncertain dynamic systems. Elsevier, Academic Press"},{"issue":"10","key":"1695_CR5","first-page":"2137","volume":"13","author":"T Allahviranloo","year":"2011","unstructured":"Allahviranloo T, Khalilpour K (2011) A numerical method for two-point fuzzy boundary value problems. World Appl Sci J 13(10):2137\u20132147","journal-title":"World Appl Sci J"},{"key":"1695_CR6","unstructured":"Barros LC, Bassanezi RC, Tonelli PA (1997) On the continuity of the Zadeh\u2019s extension. In: Proceedings of Seventh IFSA World Congress 2:3\u20138"},{"key":"1695_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53324-6","volume-title":"A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics","author":"LC Barros","year":"2017","unstructured":"Barros LC, Bassanezi RC, Lodwick WA (2017) A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics. Springer, Berlin"},{"key":"1695_CR8","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.fss.2016.04.002","volume":"309","author":"LC Barros","year":"2017","unstructured":"Barros LC, Santo Pedro F (2017) Fuzzy differential equations with interactive derivative. Fuzzy Sets Syst 309:64\u201380","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR9","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 diferentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581\u2013599","journal-title":"Fuzzy Sets Syst"},{"issue":"7","key":"1695_CR10","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1016\/j.fss.2005.09.006","volume":"157","author":"B Bede","year":"2006","unstructured":"Bede B (2006) A note on two-point boundary value problems associated with non-linear fuzzy differential equations. Fuzzy Sets Syst 157(7):986\u2013989","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35221-8","volume-title":"Mathematics of fuzzy sets and fuzzy logic","author":"B Bede","year":"2013","unstructured":"Bede B (2013) Mathematics of fuzzy sets and fuzzy logic. Springer, New York"},{"key":"1695_CR12","volume-title":"Elementary differential equations and boundary value problems","author":"WE Boyce","year":"2009","unstructured":"Boyce WE, DiPrima RC (2009) Elementary differential equations and boundary value problems. Wiley, Amsterdam"},{"key":"1695_CR13","doi-asserted-by":"crossref","unstructured":"Carlsson C, Full\u00e9r R, Majlender P (2004) Additions of completely correlated fuzzy numbers. In: Proceedings of 2004 IEEE international conference on fuzzy systems 1:535\u2013539","DOI":"10.1109\/FUZZY.2004.1375791"},{"key":"1695_CR14","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.chaos.2006.10.043","volume":"38","author":"Y Chalco-Cano","year":"2008","unstructured":"Chalco-Cano Y, Roman-Flores H (2008) On new solutions of fuzzy differential equations. Chaos Solit Fract 38:112\u2013119","journal-title":"Chaos Solit Fract"},{"key":"1695_CR15","doi-asserted-by":"crossref","unstructured":"Esmi E, Barros LC, Wasques VF (2019) Some Notes on the Addition of Interactive Fuzzy Numbers. In: Fuzzy Techniques: Theory and Applications. Springer, New York, pp 246\u2013257","DOI":"10.1007\/978-3-030-21920-8_23"},{"key":"1695_CR16","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.fss.2017.05.017","volume":"331","author":"E Esmi","year":"2018","unstructured":"Esmi E, Sussner P, Barroso G, Barros LC (2018a) A parametrized sum of fuzzy numbers with applications to fuzzy initial value problems. Fuzzy Sets Syst 331:85\u2013104","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR17","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.ins.2017.12.051","volume":"435","author":"E Esmi","year":"2018","unstructured":"Esmi E, Santo Pedro F, Barros LC, Lodwick W (2018b) Fr\u00e9chet derivative for linearly correlated fuzzy function. Inf Sci 435:150\u2013160","journal-title":"Inf Sci"},{"key":"1695_CR18","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0165-0114(03)00180-5","volume":"143","author":"R Full\u00e9r","year":"2004","unstructured":"Full\u00e9r R, Majlender P (2004) On interactive fuzzy numbers. Fuzzy Sets Syst 143:55\u2013369","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR19","doi-asserted-by":"publisher","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 (2014) Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst 257:169\u2013183","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-22575-3","volume-title":"Fuzzy differential equations in various approaches","author":"LT Gomes","year":"2015","unstructured":"Gomes LT, Barros LC, Bede B (2015) Fuzzy differential equations in various approaches. Springer, New York"},{"key":"1695_CR21","first-page":"1","volume":"1","author":"X Guo","year":"2013","unstructured":"Guo X, Shang D (2013) Fuzzy approximate solutions of second-order fuzzy linear boundary value problems. Bound Value Probl 1:1\u201317","journal-title":"Bound Value Probl"},{"key":"1695_CR22","doi-asserted-by":"crossref","unstructured":"Ib\u00e1\u00f1ez DS (2018) PVC com condi\u00e7\u00f5es de contorno Fuzzy: Solu\u00e7\u00e3o baseada em M\u00e9todo de elementos finitos. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics 6(1):1\u20137","DOI":"10.5540\/03.2018.006.01.0421"},{"key":"1695_CR23","doi-asserted-by":"crossref","unstructured":"Ib\u00e1\u00f1ez DS, Barros LC, Meyer JFCA, Laureano EE (2018) Problema de Valor de Contorno Fuzzy: Solu\u00e7ao Baseada em Derivadas Fuzzy e M\u00e9todo de Diferen\u00e7as Finitas. In: Proceeding Series of the Brazilian society of computational and applied mathematics 6(2):1\u20137","DOI":"10.5540\/03.2018.006.02.0313"},{"key":"1695_CR24","doi-asserted-by":"crossref","unstructured":"Ib\u00e1\u00f1ez DS, Esmi E, Barros LC (2018) Linear Ordinary Differential Equations with Linearly Correlated Boundary Values. In: Proceedings of 2018 IEEE international conference on fuzzy systems (FUZZ-IEEE), 1\u20136","DOI":"10.1109\/FUZZ-IEEE.2018.8491638"},{"issue":"9","key":"1695_CR25","first-page":"583","volume":"72","author":"A Khastan","year":"2010","unstructured":"Khastan A, Nieto JJ (2010) A boundary value problem for second order fuzzy differential equations. Nonlinear Anal Theory Methods Appl 72(9):583\u20133593","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"1","key":"1695_CR26","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.fss.2011.05.012","volume":"179","author":"D Li","year":"2011","unstructured":"Li D, Chen M, Xue X (2011) Two-point boundary value problems of uncertain dynamical systems. Fuzzy Sets Syst 179(1):50\u201361","journal-title":"Fuzzy Sets Syst"},{"issue":"17","key":"1695_CR27","doi-asserted-by":"publisher","first-page":"3627","DOI":"10.1016\/j.ins.2007.02.039","volume":"177","author":"MT Mizukoshi","year":"2007","unstructured":"Mizukoshi MT, Barros LC, Chalco-Cano Y, Rom\u00e1n-Flores H, Bassanezi RC (2007) Fuzzy differential equations and the extension principle. Inf Sci 177(17):3627\u20133635","journal-title":"Inf Sci"},{"key":"1695_CR28","unstructured":"Nagle RK, Saff EB, Snider AD (2004) Fundamentals of differential equations & boundary value problems, 4th ed. Pearson Addison Wesley"},{"issue":"2","key":"1695_CR29","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/0022-247X(78)90045-8","volume":"64","author":"HT Nguyen","year":"1978","unstructured":"Nguyen HT (1978) A note on the extension principle for fuzzy sets. J Math Anal Appl 64(2):369\u2013380","journal-title":"J Math Anal Appl"},{"key":"1695_CR30","doi-asserted-by":"crossref","unstructured":"O\u2019Regan D, Lakshmikantham V, Nieto JJ (2003) Initial and boundary value problems for fuzzy differential equations. Nonlinear Analysis: Theory, Methods & Applications 54(3):405\u2013415","DOI":"10.1016\/S0362-546X(03)00097-X"},{"key":"1695_CR31","doi-asserted-by":"crossref","unstructured":"Pinto NJB, Wasques VF, Esmi E, Barros LC, Method LS, with Interactive Fuzzy Coefficient: Application on Longitudinal Data. In: Fuzzy Information Processing. NAFIPS, (2018) Communications in computer and information science, vol 831. Springer, Cham, p 2018","DOI":"10.1007\/978-3-319-95312-0_12"},{"key":"1695_CR32","volume-title":"Boundary value problems: and partial differential equations","author":"DL Powers","year":"2009","unstructured":"Powers DL (2009) Boundary value problems: and partial differential equations. Academic Press, New York"},{"key":"1695_CR33","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1016\/0022-247X(83)90169-5","volume":"91","author":"ML Puri","year":"1983","unstructured":"Puri ML, Ralescu DA (1983) Differentials of fuzzy functions. J Math Anal Appl 91:552\u2013558","journal-title":"J Math Anal Appl"},{"key":"1695_CR34","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.fss.2018.07.009","volume":"358","author":"DE S\u00e1nchez","year":"2019","unstructured":"S\u00e1nchez DE, Barros LC, Esmi E (2019) On interactive fuzzy boundary value problems. Fuzzy Sets Syst 358:84\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"1695_CR35","doi-asserted-by":"crossref","unstructured":"Wasques VF, Esmi E, Barros LC, Sussner P (2018a) Numerical solutions for bidimensional initial value problem with interactive fuzzy numbers. In: Fuzzy information processing, Springer, Cham, pp 84\u201395","DOI":"10.1007\/978-3-319-95312-0_8"},{"key":"1695_CR36","doi-asserted-by":"crossref","unstructured":"Wasques VF, Esmi E, Barros LC, Santo\u00a0Pedro F, Sussner P (2018b) Higher order initial value problem with interactive fuzzy conditions. In: Proceedings of 2018 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 1\u20138","DOI":"10.1109\/FUZZ-IEEE.2018.8491465"},{"key":"1695_CR37","doi-asserted-by":"crossref","unstructured":"Wasques VF, Esmi E, Barros LC, Bede B (2019) Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics. In: Fuzzy Techniques: Theory and Applications, Springer International Publishing, 704\u2013715","DOI":"10.1007\/978-3-030-21920-8_62"},{"key":"1695_CR38","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.ins.2020.01.042","volume":"519","author":"VF Wasques","year":"2020","unstructured":"Wasques VF, Esmi E, Barros LC, Sussner P (2020) The generalized fuzzy derivative is interactive. Inf Sci 519:93\u2013109","journal-title":"Inf Sci"},{"key":"1695_CR39","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"1695_CR40","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199\u2013249","journal-title":"Inf Sci"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01695-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01695-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01695-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T10:23:00Z","timestamp":1644488580000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01695-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,29]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["1695"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01695-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,11,29]]},"assertion":[{"value":"19 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"1"}}