{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:48:36Z","timestamp":1772293716379,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,9,8]],"date-time":"2016-09-08T00:00:00Z","timestamp":1473292800000},"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>The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various anomalous exponents of particular cases, to predict damping of the field variable. Numerical computations of the convergence control parameter, used to evaluate the convergence of approximate series solution through minimizing error, are also presented graphically for these cases.<\/jats:p>","DOI":"10.3390\/e18090329","type":"journal-article","created":{"date-parts":[[2016,9,8]],"date-time":"2016-09-08T10:08:36Z","timestamp":1473329316000},"page":"329","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation"],"prefix":"10.3390","volume":"18","author":[{"given":"Neeraj","family":"Tripathi","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subir","family":"Das","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seng","family":"Ong","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hossein","family":"Jafari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South Africa"},{"name":"Department of Mathematics, University of Mazandaran, Babolsar 47416, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0979-5746","authenticated-orcid":false,"given":"Maysaa","family":"Al Qurashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.physleta.2007.02.004","article-title":"Application of Exp-function method to a KdV equation with variable coefficients","volume":"365","author":"Zhang","year":"2007","journal-title":"Phys. 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