{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T12:14:12Z","timestamp":1778501652971,"version":"3.51.4"},"reference-count":36,"publisher":"AIP Publishing","issue":"5","funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["231610271722"],"award-info":[{"award-number":["231610271722"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,5,1]]},"abstract":"<jats:p>In this work, a time-fractional form of Richards\u2019 equation is considered to study the infiltration phenomenon in unsaturated porous media. The memory effects in the flow process are described using the Caputo\u2013Fabrizio fractional operator. To obtain an approximate analytical solution of the governing nonlinear fractional partial differential equation, a hybrid analytical technique combining the Natural transform method and the variational iteration method is employed. The proposed Natural transform variational iteration method (NVIM) provides a rapidly convergent series solution and avoids complicated discretization or linearization procedures. A rigorous convergence and uniqueness analysis is carried out, which confirms the validity and accuracy of the proposed approach. The effectiveness and reliability of the method are demonstrated through the solution of the considered problem. The obtained solutions are illustrated through graphical representations using MATHEMATICA, where a comparison between the approximate analytical solution and the exact solution is carried out to validate the accuracy and effectiveness of the proposed method. In addition, the influence of the fractional parameter and other model parameters on the infiltration process is analyzed through graphical illustrations. The results demonstrate that the proposed approach provides accurate and efficient solutions and can serve as a useful analytical tool for solving nonlinear fractional differential equations arising in groundwater hydrology and related physical processes.<\/jats:p>","DOI":"10.1063\/5.0323875","type":"journal-article","created":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T12:04:11Z","timestamp":1778501051000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Fractional approach to solve water infiltration problem in an unsaturated porous medium by combined Natural transform and variational iteration method"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1022-9696","authenticated-orcid":false,"given":"Mahesh Puri","family":"Goswami","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Mohanlal Sukhadia University 1 , Udaipur 313001,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3057-475X","authenticated-orcid":false,"given":"Sonu","family":"Jatrana","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Mohanlal Sukhadia University 1 , Udaipur 313001,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5657-3367","authenticated-orcid":false,"given":"Mahaveer Prasad","family":"Yadav","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amity University Rajasthan 2 , Jaipur 302017,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"2026051108040884800_c1"},{"issue":"2","key":"2026051108040884800_c2","doi-asserted-by":"publisher","first-page":"69","DOI":"10.3934\/jcd.2022001","article-title":"A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards\u2019 equation","volume":"9","year":"2022","journal-title":"J. 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