{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T20:34:04Z","timestamp":1789763644402,"version":"4.0.1"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,22]],"date-time":"2017-07-22T00:00:00Z","timestamp":1500681600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian\u2019s decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter \u210f  and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.<\/jats:p>","DOI":"10.3390\/e19070375","type":"journal-article","created":{"date-parts":[[2017,7,24]],"date-time":"2017-07-24T10:04:06Z","timestamp":1500890646000},"page":"375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships"],"prefix":"10.3390","volume":"19","author":[{"given":"Jagdev","family":"Singh","sequence":"first","affiliation":[{"name":"Department of Mathematics, JECRC University, Jaipur, Rajasthan 303905, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Devendra","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, JECRC University, Jaipur, Rajasthan 303905, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0979-5746","authenticated-orcid":false,"given":"Maysaa Al","family":"Qurashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11495, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukar\u0131yurtcu Mahallesi Mimar Sinan Caddesi No: 4, Etimesgut 06790, Turkey"},{"name":"Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest 76911, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Machado, J.A.T., and Lopes, A.M. (2017). Fractional Jensen\u2013Shannon analysis of the scientific output of researchers in fractional calculus. Entropy, 19.","DOI":"10.3390\/e19030127"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8278","DOI":"10.3390\/e17127877","article-title":"Pathological brain detection by a novel image feature-fractional Fourier entropy","volume":"17","author":"Wang","year":"2015","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhan, X., Ma, J., and Ren, W. (2017). Research entropy complexity about the nonlinear dynamic delay game model. 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