{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:47Z","timestamp":1760243447998,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T00:00:00Z","timestamp":1661472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["72031009"],"award-info":[{"award-number":["72031009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The terminal value problem of differential equations has an important application background. In this paper, we are concerned with the terminal value problem of a first-order differential equation. Some sufficient conditions are given to obtain the existence and uniqueness results of solutions to the problem. Firstly, some comparison lemmas are established; secondly, an iterative technique and fixed point method are used to set up the main results; Finally, an example is provided to illustrate the application of the main results.<\/jats:p>","DOI":"10.3390\/axioms11090435","type":"journal-article","created":{"date-parts":[[2022,8,28]],"date-time":"2022-08-28T21:22:56Z","timestamp":1661721776000},"page":"435","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Uniqueness of Solution to a Terminal Value Problem of First-Order Differential Equation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1208-0509","authenticated-orcid":false,"given":"Yuqiang","family":"Feng","sequence":"first","affiliation":[{"name":"School of Science, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Pan","sequence":"additional","affiliation":[{"name":"Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Jiang","sequence":"additional","affiliation":[{"name":"Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,26]]},"reference":[{"key":"ref_1","first-page":"897","article-title":"Hybrid collocation method for solving terminal value problemsof a class of fractional differential eqautions","volume":"56","author":"Wang","year":"2018","journal-title":"J. Jilin Univ. (Sci. Ed.)"},{"key":"ref_2","first-page":"4","article-title":"Existence of solutions of terminal value problem for nonlinear first order differential equations systems in Banach spaces","volume":"12","author":"Zhang","year":"2010","journal-title":"J. Chuzhou Univ."},{"key":"ref_3","first-page":"68","article-title":"The method of quasi-upper and lower solutions for terminal value problems of differential equations with discontinuous terms","volume":"42","author":"Wang","year":"2009","journal-title":"J. Math. Study"},{"key":"ref_4","first-page":"264","article-title":"Maximal and minmal solutions of terminal value problems for differential eqautions in Banach spaces","volume":"19","author":"Zhou","year":"1999","journal-title":"J. Syst. Sci. Math. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.3906\/mat-1512-90","article-title":"Terminal value problem for causal differential equations with a caputofractional derivative","volume":"41","author":"Yakar","year":"2017","journal-title":"Turk. J. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.aml.2015.08.008","article-title":"A note on terminal value problems for fractional differential equations on infinite interval","volume":"52","author":"Shah","year":"2016","journal-title":"Appl. Math. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/0362-546X(81)90011-0","article-title":"On the theory of terminal value problems for ordinary differential equations","volume":"5","author":"Aftabizadeh","year":"1981","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Benchohra, M., Bouriah, S., and Nieto, J.J. (2019). Terminal value problem for differential equations with Hilfer\u2013Katugampola fractional derivative. Symmetry, 11.","DOI":"10.3390\/sym11050672"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12963","DOI":"10.1002\/mma.7600","article-title":"Terminal value problem for a generalized fractional ordinary differential equation","volume":"44","author":"Li","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.apnum.2020.05.007","article-title":"Collocation methods for terminal value problems of tempered fractional differential equations","volume":"156","author":"Babak","year":"2020","journal-title":"Appl. Numer. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/435\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:16:07Z","timestamp":1760141767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,26]]},"references-count":10,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["axioms11090435"],"URL":"https:\/\/doi.org\/10.3390\/axioms11090435","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,8,26]]}}}