{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T04:35:45Z","timestamp":1770352545966,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,5]],"date-time":"2015-10-05T00:00:00Z","timestamp":1444003200000},"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 article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conduction of the fractal temperature field in homogeneous media.<\/jats:p>","DOI":"10.3390\/e17106753","type":"journal-article","created":{"date-parts":[[2015,10,5]],"date-time":"2015-10-05T10:26:41Z","timestamp":1444040801000},"page":"6753-6764","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":91,"title":["Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains"],"prefix":"10.3390","volume":"17","author":[{"given":"Yu","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School (DEIM), University \"La Tuscia\", Largo dell'Universit\u00e0 s.n.c., Viterbo 01100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0009-4599","authenticated-orcid":false,"given":"Xiao-Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou 221008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"180601","DOI":"10.1103\/PhysRevLett.89.180601","article-title":"Heat conduction and entropy production in a one-dimensional hard-particle gas","volume":"89","author":"Grassberger","year":"2002","journal-title":"Phys. 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