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Under this proposed derivative, differentiation of fuzzy exponential function is estimated. The concept is applied for solving second-order linear fuzzy differential equation. The proposed approaches are applied to spring mass system dynamics in fuzzy environment. Lastly, numerical illustrations on second-order fuzzy differential equations are shown using analytical technique and graphically the results are displayed. <\/jats:p>","DOI":"10.1142\/s1752890924500223","type":"journal-article","created":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T09:28:25Z","timestamp":1726046905000},"source":"Crossref","is-referenced-by-count":2,"title":["Analysis of Second-Order Linear Fuzzy Differential Equation Under an Innovative Fuzzy Derivative Approach and Its Application"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7059-8373","authenticated-orcid":false,"given":"K.","family":"Rangarajan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai \u2013 602105, Tamilnadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6515-0822","authenticated-orcid":false,"given":"Payal","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences and Humanities, PIET, Parul University, Vadodara 391760, Gujarat, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1390-3551","authenticated-orcid":false,"given":"Soheil","family":"Salahshour","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey"},{"name":"Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4690-2598","authenticated-orcid":false,"given":"Sankar Prasad","family":"Mondal","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, WestBengal, India"}]}],"member":"219","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"S1752890924500223BIB001","doi-asserted-by":"publisher","DOI":"10.1177\/09544062211012723"},{"key":"S1752890924500223BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-020-04583-7"},{"key":"S1752890924500223BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.triboint.2024.109509"},{"key":"S1752890924500223BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-024-12962-9"},{"key":"S1752890924500223BIB005","first-page":"1","author":"Sen B.","year":"2024","journal-title":"Int. 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