{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T12:44:19Z","timestamp":1772109859370,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T00:00:00Z","timestamp":1591228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11661016"],"award-info":[{"award-number":["11661016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Training Object of High Level and Innovative Talents of Guizhou Province","award":["(2016)4006"],"award-info":[{"award-number":["(2016)4006"]}]},{"name":"Major Research Project 186 of Innovative Group in Guizhou Education Department","award":["2018)012"],"award-info":[{"award-number":["2018)012"]}]},{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-18-0308"],"award-info":[{"award-number":["APVV-18-0308"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003194","name":"Agent\u00fara Ministerstva \u0160kolstva, Vedy, V\u00fdskumu a \u0160portu SR","doi-asserted-by":"publisher","award":["1\/0358\/20"],"award-info":[{"award-number":["1\/0358\/20"]}],"id":[{"id":"10.13039\/501100003194","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003194","name":"Agent\u00fara Ministerstva \u0160kolstva, Vedy, V\u00fdskumu a \u0160portu SR","doi-asserted-by":"publisher","award":["2\/0127\/20"],"award-info":[{"award-number":["2\/0127\/20"]}],"id":[{"id":"10.13039\/501100003194","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guizhou Provincial Science and Technology Foundation","award":["[2020]1Y002"],"award-info":[{"award-number":["[2020]1Y002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The aim of this paper is to study the stability of generalized Liouville\u2013Caputo fractional differential equations in Hyers\u2013Ulam sense. We show that three types of the generalized linear Liouville\u2013Caputo fractional differential equations are Hyers\u2013Ulam stable by a    \u03c1   -Laplace transform method. We establish existence and uniqueness of solutions to the Cauchy problem for the corresponding nonlinear equations with the help of fixed point theorems.<\/jats:p>","DOI":"10.3390\/sym12060955","type":"journal-article","created":{"date-parts":[[2020,6,5]],"date-time":"2020-06-05T03:32:21Z","timestamp":1591327941000},"page":"955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Hyers\u2013Ulam Stability and Existence of Solutions to the Generalized Liouville\u2013Caputo Fractional Differential Equations"],"prefix":"10.3390","volume":"12","author":[{"given":"Kui","family":"Liu","sequence":"first","affiliation":[{"name":"College of Science, Guizhou Institute of Technology, Guiyang 550025, China"},{"name":"Department of Mathematics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7385-6737","authenticated-orcid":false,"given":"Michal","family":"Fe\u010dkan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynsk\u00e1 Dolina, 842 48 Bratislava, Slovakia"},{"name":"Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6642-1946","authenticated-orcid":false,"given":"Jinrong","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guizhou University, Guiyang 550025, China"},{"name":"School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,4]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. 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