{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T01:35:40Z","timestamp":1777599340778,"version":"3.51.4"},"reference-count":57,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Maulana Azad National Fellowship","award":["PLNG\/13\/2023-PLANNING-NMDFC\/CSIR NET JUNE 2021"],"award-info":[{"award-number":["PLNG\/13\/2023-PLANNING-NMDFC\/CSIR NET JUNE 2021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Uncert. Sys."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p> In this paper, the Riemann\u2013Liouville notion of fractional derivative is employed in a linear homogeneous fractional differential equation to manifest the uncertain phenomena. The impreciseness of the parameters and beginning values involved in the fractional differential equations is described in terms of the fuzzy numbers. Thus, the solution techniques for the fuzzy fractional differential equations are demonstrated constituting three distinct issues depending on the amalgamation of the fuzzy parameters and the beginning values. The fuzzy motivated calculus is presented in order to define the fuzzy fractional derivative using the idea of Hukuhara differentiability. Utilizing the theory of fuzzy fractional Laplace transformation, the solutions are obtained of the talked-about differential equations in relation to the Mittag\u2013Leffler function. <\/jats:p>","DOI":"10.1142\/s1752890925500138","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T10:21:23Z","timestamp":1746699683000},"source":"Crossref","is-referenced-by-count":3,"title":["Solutions of Linear Homogeneous Fuzzy Fractional Differential Equations Using the Mittag-Leffler Function"],"prefix":"10.1142","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5513-4095","authenticated-orcid":false,"given":"Mostafijur","family":"Rahaman","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Liberal Arts & Sciences, Mohan Babu University, Tirupati-517102, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7179-984X","authenticated-orcid":false,"given":"Kamal Hossain","family":"Gazi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, Nadia, West Bengal, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3588-9693","authenticated-orcid":false,"given":"Mohammed","family":"Rabih","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9621-5383","authenticated-orcid":false,"given":"Abdul","family":"Alamin","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, Nadia, West Bengal, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3433-2252","authenticated-orcid":false,"given":"Oyoon Abdul","family":"Razzaq","sequence":"additional","affiliation":[{"name":"Department of Humanities & Social Sciences, Bahria University, Karachi 75260, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6242-0658","authenticated-orcid":false,"given":"Najeeb Alam","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Karachi, Karachi 75270, Pakistan"}]},{"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, Nadia, West Bengal, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8263-117X","authenticated-orcid":false,"given":"Shariful","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering, Science and Technology, Shibpur, Howrah, India"}]}],"member":"219","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"key":"S1752890925500138BIB001","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-017-1461-2"},{"key":"S1752890925500138BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-11662-0_15"},{"key":"S1752890925500138BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2018.04.075"},{"key":"S1752890925500138BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2019.01.013"},{"key":"S1752890925500138BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2018.11.003"},{"key":"S1752890925500138BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124572"},{"key":"S1752890925500138BIB007","doi-asserted-by":"publisher","DOI":"10.2298\/TSCI160209103K"},{"key":"S1752890925500138BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.11.029"},{"issue":"1","key":"S1752890925500138BIB009","first-page":"167","volume":"34","author":"Yang Z.","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"S1752890925500138BIB010","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/6457548"},{"key":"S1752890925500138BIB011","first-page":"54","volume":"347","author":"Hoa N. V.","year":"2017","journal-title":"Fuzzy Sets Syst."},{"key":"S1752890925500138BIB012","first-page":"159","volume":"5","author":"Mukherjee S.","year":"2024","journal-title":"J. Fuzzy Ext. Appl."},{"key":"S1752890925500138BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-008-0397-6"},{"key":"S1752890925500138BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120308"},{"key":"S1752890925500138BIB015","first-page":"1","volume":"2013","author":"Allahviranloo T.","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"S1752890925500138BIB016","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/454969"},{"key":"S1752890925500138BIB017","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130831"},{"key":"S1752890925500138BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.08.001"},{"key":"S1752890925500138BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.109397"},{"key":"S1752890925500138BIB020","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/7275934"},{"key":"S1752890925500138BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2020.11.017"},{"key":"S1752890925500138BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-022-00353-y"},{"key":"S1752890925500138BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-023-00364-3"},{"key":"S1752890925500138BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-011-0743-y"},{"key":"S1752890925500138BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.07.005"},{"key":"S1752890925500138BIB026","doi-asserted-by":"publisher","DOI":"10.3390\/math8122166"},{"key":"S1752890925500138BIB027","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X23400868"},{"key":"S1752890925500138BIB028","first-page":"1","volume":"10","author":"Askari S.","year":"2019","journal-title":"Int. Trans. J. Eng. Manage. Appl. Sci. Tech."},{"key":"S1752890925500138BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.10.012"},{"key":"S1752890925500138BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.10.002"},{"key":"S1752890925500138BIB031","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2331-x"},{"issue":"2","key":"S1752890925500138BIB032","first-page":"57","volume":"16","author":"Armand A.","year":"2019","journal-title":"Iranian J. Fuzzy Syst."},{"key":"S1752890925500138BIB033","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.018.01.07"},{"key":"S1752890925500138BIB034","doi-asserted-by":"publisher","DOI":"10.1109\/JEEIT.2019.8717378"},{"key":"S1752890925500138BIB035","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-151940"},{"issue":"2","key":"S1752890925500138BIB036","first-page":"71","volume":"11","author":"Ahmady N.","year":"2019","journal-title":"Int. J. Ind. Math."},{"key":"S1752890925500138BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-020-00241-3"},{"issue":"39","key":"S1752890925500138BIB038","first-page":"1","volume":"46","author":"Rahaman M.","year":"2021","journal-title":"S\u0101dhan\u0101"},{"key":"S1752890925500138BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.04.005"},{"key":"S1752890925500138BIB040","doi-asserted-by":"publisher","DOI":"10.1016\/j.cjph.2024.04.019"},{"key":"S1752890925500138BIB041","first-page":"151","volume":"18","author":"Beigmohamadi R.","year":"2021","journal-title":"Iran. J. Fuzzy Syst."},{"key":"S1752890925500138BIB042","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.09.006"},{"key":"S1752890925500138BIB043","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.09.015"},{"key":"S1752890925500138BIB044","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2020.05.004"},{"issue":"2","key":"S1752890925500138BIB045","volume":"18","author":"Rahaman M.","year":"2024","journal-title":"J. Uncertain Syst."},{"key":"S1752890925500138BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112751"},{"key":"S1752890925500138BIB047","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract9020102"},{"key":"S1752890925500138BIB048","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/295432"},{"key":"S1752890925500138BIB049","doi-asserted-by":"publisher","DOI":"10.1515\/fca-2018-0072"},{"key":"S1752890925500138BIB050","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1914-2"},{"key":"S1752890925500138BIB051","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1693-9"},{"key":"S1752890925500138BIB052","doi-asserted-by":"publisher","DOI":"10.1080\/0020739X.2013.851803"},{"key":"S1752890925500138BIB053","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1923-1"},{"key":"S1752890925500138BIB054","first-page":"14","volume":"2019","author":"Mondal S. P.","year":"2019","journal-title":"Adv. Fuzzy Syst."},{"key":"S1752890925500138BIB055","doi-asserted-by":"publisher","DOI":"10.1002\/int.22180"},{"key":"S1752890925500138BIB056","doi-asserted-by":"publisher","DOI":"10.3390\/sym11020248"},{"key":"S1752890925500138BIB057","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-32-9515-5_40"}],"container-title":["Journal of Uncertain Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1752890925500138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T07:26:34Z","timestamp":1758785194000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1752890925500138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,3]]},"references-count":57,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S1752890925500138"],"URL":"https:\/\/doi.org\/10.1142\/s1752890925500138","relation":{},"ISSN":["1752-8909","1752-8917"],"issn-type":[{"value":"1752-8909","type":"print"},{"value":"1752-8917","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,3]]},"article-number":"2550013"}}