{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:27:01Z","timestamp":1777703221061,"version":"3.51.4"},"reference-count":32,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:00:00Z","timestamp":1559088000000},"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":[[2019,6,11]]},"abstract":"<jats:p>In this paper, we consider Goursat boundary value problems for fuzzy delay fractional partial differential equations under Caputo gH-derivatives. Firstly, the unique solvability of the problems in finite domain is considered. Secondly, by restricting the force function and boundary conditions by exponential growth and using fixed point approach, the existence and the Ulam-Hyers stability of fuzzy mild solutions of the problem in infinite domain are investigated in two types with different geometric behaviors. It is necessary to implement that in many engineering applications, e.g. numerical solutions of a fuzzy dynamical system, the object of optimization problems or the trajectory of a economical dynamics etc., where finding the exact solution is more difficult than solving its approximate solutions, Ulam-Hyers stability is quite useful. Finally, as usual some examples are given to illustrate the obtained theoretical results.<\/jats:p>","DOI":"10.3233\/jifs-182590","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:40:11Z","timestamp":1559302811000},"page":"6295-6306","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["On Goursat problem for fuzzy delay fractional hyperbolic partial differential equations"],"prefix":"10.1177","volume":"36","author":[{"given":"Nguyen Thi Kim","family":"Son","sequence":"first","affiliation":[{"name":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hoang Thi Phuong","family":"Thao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Foreign Language Specialized School, Hanoi, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,5,29]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4036-9"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.11.029"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2017.09.039"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.03.011"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2016.2554156"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.11.013"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130831"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.11.009"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.12.002"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00323-6"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.04.010"},{"key":"e_1_3_2_13_2","article-title":"Course in Mathematical Analysis","volume":"3","author":"Goursat E.A.","year":"1923","unstructured":"E.A.Goursat, Course in Mathematical Analysis, Vol. 3: Variation of Solutions and Partial Diffferential Equations of the Second Order and Integral Equations and Calculus of Variations Paris: Gauthier-Villars, 1923.","journal-title":"Variation of Solutions and Partial Diffferential Equations of the Second Order and Integral Equations and Calculus of Variations Paris: Gauthier-Villars"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.01.009"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141315"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.08.006"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.09.006"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151623"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.06.018"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.11.008"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151547"},{"key":"e_1_3_2_22_2","first-page":"1","article-title":"Existence and uniqueness results for fractional differential equations with uncertainty","volume":"112","author":"Salahshour S.","year":"2012","unstructured":"S.Salahshour, T.Allahviranloo, S.Abbasbandy and D.Baleanu, Existence and uniqueness results for fractional differential equations with uncertainty, Adv Differ Equ 112 (2012), 1\u201312.","journal-title":"Adv Differ Equ"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.3390\/e17020885"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.3390\/e18030068"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2016.10.044"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-152073"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.01.002"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.07.019"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-152073"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.01.002"},{"key":"e_1_3_2_31_2","volume-title":"A Concise Handbook of Mathematics, Physics, and Engineering Sciences","author":"Polyanin A.D.","year":"2017","unstructured":"A.D.Polyanin and A.I.Chernoutsan, A Concise Handbook of Mathematics, Physics, and Engineering Sciences, CRC Press, 2017."},{"issue":"4","key":"e_1_3_2_32_2","first-page":"79","article-title":"On impulsive fuzzy functional differential equations","volume":"13","author":"Vu H.","year":"2016","unstructured":"H.Vu and N.V.Hoa, On impulsive fuzzy functional differential equations, Iran J Fuzzy Syst 13(4) (2016), 79\u201394.","journal-title":"Iran J Fuzzy Syst"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-171070"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182590","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-182590","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182590","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:11Z","timestamp":1777455491000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-182590"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,29]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6,11]]}},"alternative-id":["10.3233\/JIFS-182590"],"URL":"https:\/\/doi.org\/10.3233\/jifs-182590","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,29]]}}}