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The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet\u2010based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional\u2010order delay differential equations.<\/jats:p>","DOI":"10.1155\/2022\/3218213","type":"journal-article","created":{"date-parts":[[2022,3,14]],"date-time":"2022-03-14T18:35:26Z","timestamp":1647282926000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of the Fractional\u2010Order Delay Differential Equations by the Numerical Method"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0284-6750","authenticated-orcid":false,"given":"Saadia","family":"Masood","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-9381","authenticated-orcid":false,"given":"Muhammad","family":"Naeem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Ullah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0584-1445","authenticated-orcid":false,"given":"Saima","family":"Mustafa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3902-1944","authenticated-orcid":false,"given":"Abdul","family":"Bariq","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,3,14]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10231-003-0085-1"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/8.489308"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.1478062"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym13050886"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.2514\/3.9007"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.3390\/e23081086"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/7117064"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.3390\/math9182326"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/1537958"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym13050784"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3101682"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-2664-6_7"},{"key":"e_1_2_10_13_2","unstructured":"HeJ. 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