{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T10:00:59Z","timestamp":1771668059312,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T00:00:00Z","timestamp":1726790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science, Research and Innovation Fund (NSRF), and King Mongkut\u2019s University of Technology North Bangkok","award":["KMUTNB-FF-67-B-26"],"award-info":[{"award-number":["KMUTNB-FF-67-B-26"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges. The first challenge is to deal with the two types of fuzzy gH-differentiability: (i)-differentiability and (ii)-differentiability. The sign of coefficients in Goursat problems and gH-differentiability produces sixteen possible cases. The existing literature does not afford a solution method that addresses all the possible cases of this problem. The second challenge is the mixed derivative term in Goursat problems with fuzzy boundary conditions. Therefore, we propose to discuss the solutions of fuzzy Goursat problems with gH-differentiability. We will discuss the solutions of fuzzy Goursat problems in series form with natural transform and Adomian decompositions. To demonstrate the usability of the established solution methods, we will provide some numerical examples.<\/jats:p>","DOI":"10.3390\/axioms13090645","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T10:49:48Z","timestamp":1726829388000},"page":"645","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solutionsof Fuzzy Goursat Problems with Generalized Hukuhara (gH)-Differentiability Concept"],"prefix":"10.3390","volume":"13","author":[{"given":"Noor","family":"Jamal","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3904-8442","authenticated-orcid":false,"given":"Muhammad","family":"Sarwar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18000, Pakistan"},{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0735-6520","authenticated-orcid":false,"given":"Kamaleldin","family":"Abodayeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0547-0821","authenticated-orcid":false,"given":"Manel","family":"Hleili","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"given":"Saowaluck","family":"Chasreechai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"},{"name":"Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"additional","affiliation":[{"name":"Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"},{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2695","DOI":"10.3934\/math.2024134","article-title":"Solution of linear correlated fuzzy differential equa-tions in the linear correlated fuzzy spaces","volume":"9","author":"Jamal","year":"2023","journal-title":"AIMS Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1007\/s40815-017-0367-1","article-title":"Fuzzy Stochastic Data Envelopment Analysis with Undesirable Outputs and its Application to Banking Industry","volume":"20","author":"Nasseri","year":"2017","journal-title":"Int. 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