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We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.<\/jats:p>","DOI":"10.1155\/2020\/2854574","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T18:31:19Z","timestamp":1582914679000},"page":"1-12","source":"Crossref","is-referenced-by-count":6,"title":["Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3356-4825","authenticated-orcid":true,"given":"Josef","family":"Rebenda","sequence":"first","affiliation":[{"name":"CEITEC BUT, Brno University of Technology, Purky\u0148ova 656\/123, 61200 Brno, Czech Republic"},{"name":"Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick\u00e1 8, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zuzana","family":"P\u00e1t\u00edkov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Informatics, Tomas Bata University in Zl\u00edn, Nad Str\u00e1n\u011bmi 4511, Zl\u00edn 76005, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","first-page":"121","volume":"26","year":"2011","journal-title":"Nonlinear Dynamics"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2019.102998"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.07.051"},{"key":"4","year":"1999"},{"key":"5","year":"1991"},{"key":"6","year":"1993"},{"key":"8","first-page":"83","volume":"17","year":"2015","journal-title":"Communications-Scientific Letters of the University of \u017dilina"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.2298\/fil1715725r"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.12988\/ams.2016.66188"},{"key":"14","first-page":"1","volume":"69","year":"2013","journal-title":"Advances in Difference Equations"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2016.12.027"},{"key":"16","year":"2003"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2005.12.004"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-1961-3"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.08.084"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/01630560902987576"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2854574.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2854574.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2854574.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T18:30:50Z","timestamp":1583260250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/2854574\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,28]]},"references-count":16,"alternative-id":["2854574","2854574"],"URL":"https:\/\/doi.org\/10.1155\/2020\/2854574","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,28]]}}}