{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:19Z","timestamp":1777704319524,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,8,11]],"date-time":"2018-08-11T00:00:00Z","timestamp":1533945600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10]]},"abstract":"<jats:p>In this paper, we introduce a fuzzy Mellin transform method for solving Hermite fuzzy differential equations. The fuzzy Mellin transform reduce the problem of solving a Hermite fuzzy differential equation to a problem of solving a difference equation, whose inverse transform gives the solution of the fuzzy differential equation at hands. Under some conditions, we also give some Hyers-Ulam stability result of Hermite fuzzy differential equations.<\/jats:p>","DOI":"10.3233\/jifs-18523","type":"journal-article","created":{"date-parts":[[2018,8,14]],"date-time":"2018-08-14T15:56:28Z","timestamp":1534262188000},"page":"3721-3731","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Hyers-Ulam stability of Hermite fuzzy differential equations and fuzzy Mellin transform"],"prefix":"10.1177","volume":"35","author":[{"given":"Wenjuan","family":"Ren","sequence":"first","affiliation":[{"name":"Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China"}]},{"given":"Zhanpeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China"}]},{"given":"Xian","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China"}]},{"given":"Min","family":"Qi","sequence":"additional","affiliation":[{"name":"Basic Teaching Department, Beijing College of Finance and Commerce, Beijing, PR China"}]}],"member":"179","published-online":{"date-parts":[[2018,8,11]]},"reference":[{"key":"e_1_3_1_2_2","author":"Ulam S.M.","year":"1968","unstructured":"S.M.Ulam, A Collection of Mathematical Problems, New York, 1968.","journal-title":"A Collection of Mathematical Problems"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.27.4.222"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/00210064"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1978-0507327-1"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(82)90048-9"},{"key":"e_1_3_1_7_2","first-page":"1","article-title":"Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces","volume":"51","author":"Xu T.Z.","year":"2010","unstructured":"T.Z.Xu, J.M.Rassias and W.X.Xu, Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces, Journal of Mathematical Physics 51 (2010), 1\u201319.","journal-title":"Journal of Mathematical Physics"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-015-0576-3"},{"key":"e_1_3_1_9_2","first-page":"697","article-title":"Direct and fixed point approaches to the stability of an AQ-functional equation in non-Archimedean normed spaces","volume":"17","author":"Xu T.Z.","year":"2014","unstructured":"T.Z.Xu, Z.P.Yang and J.M.Rassias, Direct and fixed point approaches to the stability of an AQ-functional equation in non-Archimedean normed spaces, Journal of Computional Analysis and Applications 17 (2014), 697\u2013706.","journal-title":"Journal of Computional Analysis and Applications"},{"key":"e_1_3_1_10_2","first-page":"147","volume":"74","author":"Jung S.M.","year":"2017","unstructured":"S.M.Jung and J.Roh, Hyers-Ulam stability of the time independent Schrodinger equations, Applied Mathematics Letters 74 (2017), 147\u2013153.","journal-title":"Hyers-Ulam stability of the time independent Schrodinger equations, Applied Mathematics Letters"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-013-0083-9"},{"key":"e_1_3_1_12_2","first-page":"126","article-title":"On the Hyers-Ulam stability of the functional equations that have the quadratic property","volume":"222","author":"Jung S.M.","year":"1998","unstructured":"S.M.Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, Journal ofMath-ematical Analysis and Applications 222 (1998), 126\u2013137.","journal-title":"Journal ofMath-ematical Analysis and Applications"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.09.030"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.01.002"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-009-9351-7"},{"key":"e_1_3_1_16_2","first-page":"181","article-title":"A new method for solving fuzzy linear differential equations","volume":"92","author":"Allahviranloo T.","year":"2011","unstructured":"T.Allahviranloo, S.Abbasbandy, S.Salahshour and A.Hakimzadeh, A new method for solving fuzzy linear differential equations, Soft Computing 92 (2011), 181\u2013197.","journal-title":"Soft Computing"},{"key":"e_1_3_1_17_2","first-page":"1247","volume":"15","author":"Allahviranloo T.","year":"2011","unstructured":"T.Allahviranloo and S.Salahshour, Euler method for solving hybrid fuzzy differential equation, Soft Computing 15 (2011), 1247\u20131253.","journal-title":"Euler method for solving hybrid fuzzy differential equation, Soft Computing"},{"key":"e_1_3_1_18_2","doi-asserted-by":"crossref","first-page":"2859","DOI":"10.1016\/j.na.2009.11.029","article-title":"On the concept of solution for fractional differential equations with uncertainty.","volume":"72","author":"Agarwal R.P.","year":"2010","unstructured":"R.P.Agarwal, V.Lakshmikantham and J.J.Nieto, On the concept of solution for fractional differential equations with uncertainty. Nonlinear Analysis: Theory, Methods and Applications 72 (2010), 2859\u20132862.","journal-title":"Nonlinear Analysis: Theory, Methods and Applications"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.08.001"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)00016-4"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00355-8"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-012-1120-1"},{"key":"e_1_3_1_23_2","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","article-title":"Generalized Hukuhara differentiability of interval-valued functions and interval differential equations.","volume":"71","author":"Stefanini L.","year":"2009","unstructured":"L.Stefanini and B.Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis: Theory, Methods and Applications 71 (2009), 1311\u20131328.","journal-title":"Nonlinear Analysis: Theory, Methods and Applications"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00323-6"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2052-y"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130831"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488506003868"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.11.030"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.03.031"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14058-7_53"},{"key":"e_1_3_1_31_2","first-page":"1372","volume":"17","author":"Salahshour S.","year":"2012","unstructured":"S.Salahshour, T.Allahviranloo and S.Abbasbandy, Solving fuzzy fractional differential equation by fuzzy Laplace transforms, Communications in Nonlinear Science and Numerical Simularion 17 (2012), 1372\u20131381.","journal-title":"Solving fuzzy fractional differential equation by fuzzy Laplace transforms, Communications in Nonlinear Science and Numerical Simularion"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.11.022"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00001-X"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02649101"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1224-x"},{"key":"e_1_3_1_36_2","first-page":"145","volume":"17","author":"Salahshour S.","year":"2013","unstructured":"S.Salahshour and T.Allahviranloo, Applications of fuzzy Laplace transforms, Soft Computing 17 (2013), 145\u2013158.","journal-title":"Applications of fuzzy Laplace transforms, Soft Computing"},{"key":"e_1_3_1_37_2","article-title":"A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform","author":"Gouyandeh Z.","year":"2016","unstructured":"Z.Gouyandeh, T.Allahviranloo, S.Abbasbandy and A.Armand, A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets and Systems (2016). 10.1016\/ j.fss.2016.04.010","journal-title":"Fuzzy Sets and Systems"},{"key":"e_1_3_1_38_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-016-1027-8"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.05.002"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18523","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18523","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18523","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:56Z","timestamp":1777455656000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18523"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,11]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["10.3233\/JIFS-18523"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18523","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,11]]}}}