{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T07:28:46Z","timestamp":1768289326406,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,18]],"date-time":"2022-08-18T00:00:00Z","timestamp":1660780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["2019-03907"],"award-info":[{"award-number":["2019-03907"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A system of generalized fuzzy random differential equations with boundary conditions is investigated, which is a fuzzy version of a system of general random differential equations. We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we define the operators that are of integral type. Furthermore, these operators are related to a part of random differential equations (RDE). For the desired system with boundary conditions, we study the suitable integral operators associated with a large family of random differential equations. Finally, we prove the existence of a unique random solution (EURS).<\/jats:p>","DOI":"10.3390\/axioms11080414","type":"journal-article","created":{"date-parts":[[2022,8,18]],"date-time":"2022-08-18T21:39:21Z","timestamp":1660858761000},"page":"414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Fuzzy Random Boundary Value Problem"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Section of Mathematics, International Telematic, University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2817-9711","authenticated-orcid":false,"given":"Reza","family":"Chaharpashlou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jundi-Shapur University of Technology, Dezful 64615-334, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6770-6951","authenticated-orcid":false,"given":"Reza","family":"Saadati","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7098-8059","authenticated-orcid":false,"given":"Chenkuan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,18]]},"reference":[{"key":"ref_1","first-page":"280","article-title":"On the notion of a random normed space","volume":"149","year":"1963","journal-title":"Dokl. Akad. Nauk. USSR"},{"key":"ref_2","first-page":"351","article-title":"Almost Sure Convergence in Linear Spaces of Random Variables","volume":"15","year":"1970","journal-title":"Teor. Verojat. Primen."},{"key":"ref_3","first-page":"217","article-title":"Linear operators in random normed spaces","volume":"17","author":"Radu","year":"1973","journal-title":"Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.)"},{"key":"ref_4","first-page":"429","article-title":"Fuzzy linear operators and fuzzy normed linear spaces","volume":"86","author":"Cheng","year":"1994","journal-title":"Bull. Calcutta Math. Soc."},{"key":"ref_5","unstructured":"Bharucha-Reid, A.T. (1972). Random Integral Equations, Academic Press."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Skorohod, A. (1985). Random Linear Operators, Reidel.","DOI":"10.1007\/978-94-009-6063-3"},{"key":"ref_7","first-page":"12","article-title":"Solution to random differential equations with boundary conditions","volume":"110","author":"Tchier","year":"2017","journal-title":"Electron. Differ. Equ."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Cho, Y.J., Rassias, T.M., and Saadati, R. (2018). Fuzzy Operator Theory in Mathematical Analysis, Springer.","DOI":"10.1007\/978-3-319-93501-0"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5488","DOI":"10.22436\/jnsa.009.09.16","article-title":"On fuzzy normed algebras","volume":"9","author":"Tudor","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Klement, E.P., Mesiar, R., and Pap, E. (2000). Triangular Norms, Kluwer Academic.","DOI":"10.1007\/978-94-015-9540-7"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Denkowski, Z., Mig\u00f3rski, S., and Papageorgiou, N.S. (2003). An Introduction to Nonlinear Analysis Theory, Springer.","DOI":"10.1007\/978-1-4419-9158-4"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"67","DOI":"10.22436\/jmcs.023.01.07","article-title":"Numerical solutions of fuzzy integro-differential equations of the second kind","volume":"23","author":"Issa","year":"2021","journal-title":"J. Math. Comput. Sci."},{"key":"ref_13","first-page":"103","article-title":"Solution and intuitionistic fuzzy stability of 3-dimensional cubic functional equation: Using two different methods","volume":"25","author":"Jakhar","year":"2022","journal-title":"J. Math. Comput. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"84","DOI":"10.22436\/jmcs.025.01.07","article-title":"Fixed point for fuzzy mappings in different generalized types of metric spaces","volume":"25","author":"Kamal","year":"2022","journal-title":"J. Math. Comput. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"373904","DOI":"10.1155\/2012\/373904","article-title":"Approximation of homomorphisms and derivations on non-Archimedean Lie C*-algebras via fixed point method","volume":"2012","author":"Cho","year":"2012","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1910","DOI":"10.1016\/j.aml.2011.05.017","article-title":"Stability of some set-valued functional equations","volume":"24","author":"Park","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"196","DOI":"10.22436\/jnsa.014.04.02","article-title":"SIQR dynamics in a random network with heterogeneous connections with infection age","volume":"14","author":"Yan","year":"2021","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"136","DOI":"10.22436\/jmcs.021.02.05","article-title":"Solving fuzzy Burgers equation by variational iteration method","volume":"21","author":"Harir","year":"2020","journal-title":"J. Math. Comput. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"296","DOI":"10.22436\/jmcs.021.04.03","article-title":"Solvability of a boundary value problem of self-reference functional differential equation with infinite point and integral conditions","volume":"21","author":"Ahmed","year":"2020","journal-title":"J. Math. Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"231","DOI":"10.22436\/jmcs.021.03.06","article-title":"Extended cubic B-spline method for solving a system of non-linear second-order boundary value problems","volume":"21","author":"Heilat","year":"2020","journal-title":"J. Math. Comput. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"283","DOI":"10.22436\/jmcs.020.04.02","article-title":"A finite-difference scheme for initial boundary value problem of the Gamma equation in the pricing of financial derivatives","volume":"20","author":"Hieu","year":"2020","journal-title":"J. Math. Comput. Sci."},{"key":"ref_22","first-page":"1","article-title":"Integrable solutions of functional equations","volume":"127","author":"Matkowski","year":"1975","journal-title":"Diss. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s13663-016-0590-8","article-title":"Random fixed point theorems in partially ordered metric spaces","volume":"2016","author":"Nieto","year":"2016","journal-title":"Fixed Point Theory Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/414\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:11:58Z","timestamp":1760141518000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/8\/414"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,18]]},"references-count":23,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["axioms11080414"],"URL":"https:\/\/doi.org\/10.3390\/axioms11080414","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,18]]}}}