{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:21:05Z","timestamp":1769185265008,"version":"3.49.0"},"reference-count":48,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T00:00:00Z","timestamp":1670025600000},"content-version":"vor","delay-in-days":336,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu\u2013Mihet method, which is derived from the alternative fixed\u2010 point theorem. Considering the matrix\u2010valued fuzzy k\u2010normed spaces and matrix\u2010valued fuzzy H\u2010Fox function as a control function, we investigate the existence of a unique solution and Hyers\u2013Ulam\u2010H\u2010Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.<\/jats:p>","DOI":"10.1155\/2022\/5630187","type":"journal-article","created":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T11:50:05Z","timestamp":1670068205000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Existence of a Unique Solution and the Hyers\u2013Ulam\u2010H\u2010Fox Stability of the Conformable Fractional Differential Equation by Matrix\u2010Valued Fuzzy Controllers"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2517-3365","authenticated-orcid":false,"given":"Zahra","family":"Eidinejad","sequence":"first","affiliation":[]},{"given":"Reza","family":"Saadati","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6673-3560","authenticated-orcid":false,"given":"Tofigh","family":"Allahviranloo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0354-9344","authenticated-orcid":false,"given":"Farzad","family":"Kiani","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2307-0891","authenticated-orcid":false,"given":"Samad","family":"Noeiaghdam","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9194-2009","authenticated-orcid":false,"given":"Unai","family":"Fernandez-Gamiz","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2022,12,3]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"1191","article-title":"Hadamard-type fractional calculus","volume":"38","author":"Kilbas A. A.","year":"2001","journal-title":"Journal of the Korean Mathematical Society"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0022-247x(02)00001-x"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.01.002"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.10.016"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2022584"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/8280203"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.04.049"},{"key":"e_1_2_9_8_2","first-page":"109","article-title":"Newly defined conformable derivatives","volume":"10","author":"Anderson D. R.","year":"2015","journal-title":"Advances in Dynamical Systems and Applications"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/3720471"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms10020063"},{"key":"e_1_2_9_11_2","article-title":"Fuzzy measure model for COVID-19 disease","volume":"202","author":"Ghaffari A.","year":"2021","journal-title":"Adv. Difference Equ."},{"key":"e_1_2_9_12_2","first-page":"57","article-title":"An operational method for solving fractional differential equations of an arbitrary real order","volume":"6","author":"Hadid S. B.","year":"1996","journal-title":"Panamer. Math. J."},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/950728"},{"key":"e_1_2_9_14_2","article-title":"Fixed points and the stability of Jensen\u2019s functional equation","volume":"4","author":"Cadariu L.","year":"2003","journal-title":"JIPAM. J. Inequal. Pure Appl. Math."},{"key":"e_1_2_9_15_2","first-page":"79","article-title":"Some special functions related to fractional calculus and fractional (non-integer) order control systems and equations","volume":"7","author":"Kiryakova V.","year":"2008","journal-title":"Facta Universitatis \u2013 Series: Automatic Control and Robotics"},{"key":"e_1_2_9_16_2","first-page":"363","article-title":"Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces. Uncertainty modelling, 2001 (Bratislava)","volume":"38","author":"Hadzic O.","year":"2002","journal-title":"Kybernetika"},{"key":"e_1_2_9_17_2","article-title":"Triangular norms","volume":"8","author":"Klement E. P.","year":"2000","journal-title":"Trends in Logic Studia Logica Library"},{"key":"e_1_2_9_18_2","article-title":"Probabilistic metric spaces","author":"Schweizer B.","year":"1983","journal-title":"North-Holland Series in Probability and Applied Mathematics"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9904-1968-11933-0"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jksus.2020.101246"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/abf582"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1002\/num.22587"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2"},{"key":"e_1_2_9_24_2","article-title":"Theory and applications of fractional differential equations","volume":"204","author":"Kilbas A. A.","year":"2006","journal-title":"North-Holland Mathematics Studies"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-008-9356-6"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.04.041"},{"key":"e_1_2_9_27_2","article-title":"Conformable fractional Semigroups of operators","author":"Horani M.","year":"2014","journal-title":"Functional Analysis"},{"key":"e_1_2_9_28_2","article-title":"Handbook of mathematical functions with for- mulas, graphs, and mathematical tables","author":"Abramowitz M.","year":"1964","journal-title":"National Bureau of Standards Ap- Plied Mathematics Series, 55 for Sale by the Superintendent of Documents"},{"key":"e_1_2_9_29_2","volume-title":"Basic Theory of Fractional Differential Equations","author":"Zhou Y.","year":"2017"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1515\/fca-2016-0017"},{"key":"e_1_2_9_31_2","doi-asserted-by":"publisher","DOI":"10.1515\/fca-2016-0044"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.10.014"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.05.040"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.020.02.05"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.22436\/jnsa.013.03.06"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.021.01.01"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00009-015-0523-5"},{"key":"e_1_2_9_38_2","article-title":"Ulam-Hyers-Rassias stability for nonlinear \u03a8-Hilfer stochastic fractional differential equation with uncertainty","volume":"339","author":"Chaharpashlou R.","year":"2020","journal-title":"Adv. Difference Equ."},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5765"},{"key":"e_1_2_9_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.03.026"},{"key":"e_1_2_9_41_2","doi-asserted-by":"crossref","unstructured":"AsaduzzamanMd. KilicmanA. andAliM. Z. Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument The Journal of Mathematics and Computer Science 23 no. 03 230\u2013244 https:\/\/doi.org\/10.22436\/jmcs.023.03.06.","DOI":"10.22436\/jmcs.023.03.06"},{"key":"e_1_2_9_42_2","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.016.02.03"},{"key":"e_1_2_9_43_2","article-title":"A generalized Lyapunov-type inequality in the frame of conformable derivatives","volume":"321","author":"Abdeljawad T.","year":"2017","journal-title":"Adv. Difference Equ."},{"key":"e_1_2_9_44_2","first-page":"273","article-title":"Sturm\u2019s theorems for conformable fractional differential equations","volume":"21","author":"Pospisil M.","year":"2016","journal-title":"Mathematical Communications"},{"key":"e_1_2_9_45_2","first-page":"177","article-title":"Abels formula and Wronskian for conformable fractional differential equations","volume":"13","author":"Hammad M. A.","year":"2014","journal-title":"Int. J. Differ. Equ. Appl."},{"key":"e_1_2_9_46_2","first-page":"485","article-title":"The HyersUlam stability of the conformable fractional differential equation","volume":"5","author":"Zheng A.","year":"2015","journal-title":"Math. Aeterna"},{"key":"e_1_2_9_47_2","doi-asserted-by":"publisher","DOI":"10.18576\/pfda\/020204"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2016.01.014"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/5630187","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2022\/5630187","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/5630187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:07:07Z","timestamp":1769116027000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2022\/5630187"}},"subtitle":[],"editor":[{"given":"Abdellatif","family":"Ben Makhlouf","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1155\/2022\/5630187"],"URL":"https:\/\/doi.org\/10.1155\/2022\/5630187","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"2022-05-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-06-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-12-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5630187"}}