{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:16:55Z","timestamp":1760217415760,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,12]],"date-time":"2015-06-12T00:00:00Z","timestamp":1434067200000},"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 different kinds of boundary conditions for standard and fractional diffusion and advection diffusion equations are analyzed. Near the interface between two phases there arises a transition region which state differs from the state of contacting media owing to the different material particle interaction conditions. Particular emphasis has been placed on the conditions of nonperfect diffusive contact for the time-fractional advection diffusion equation. When the reduced characteristics of the interfacial region are equal to zero, the conditions of perfect contact are obtained as a particular case.<\/jats:p>","DOI":"10.3390\/e17064028","type":"journal-article","created":{"date-parts":[[2015,6,12]],"date-time":"2015-06-12T10:56:00Z","timestamp":1434106560000},"page":"4028-4039","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Generalized Boundary Conditions for the Time-Fractional Advection Diffusion Equation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Computer Science, Jan D\u0142ugosz University in Cz\u0119stochowa, Armii Krajowej 13\/15, 42-200 Cz\u0119stochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(00)00070-3","article-title":"The random walk\u2019s guide to anomalous diffusion: A fractional dynamics approach","volume":"339","author":"Metzler","year":"2000","journal-title":"Phys. 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