{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:24:07Z","timestamp":1787329447710,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>In this paper, we consider the time fractional inverse advection-dispersion problem (TFIADP) in a quarter plane. The solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative with the Caputo fractional derivative of order $\\alpha$ ($0&lt;\\alpha&lt;1$). We show that the TFIADP is severely ill-posed, and we further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, one numerical example is given to show that the proposed numerical method is effective.<\/jats:p>","DOI":"10.1137\/100783042","type":"journal-article","created":{"date-parts":[[2011,10,4]],"date-time":"2011-10-04T21:25:33Z","timestamp":1317763533000},"page":"1972-1990","source":"Crossref","is-referenced-by-count":29,"title":["A New Regularization Method for the Time Fractional Inverse Advection-Dispersion Problem"],"prefix":"10.1137","volume":"49","author":[{"given":"G. H.","family":"Zheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,10,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/env.770"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-007-0013-4"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597331394"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/num.20112"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1002\/num.20169"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02936577"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/S1446181100008282"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00181-9"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-007-0076-z"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02936089"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.06.005"},{"key":"R12","first-page":"267","volume":"27","author":"Lu X. Z.","year":"2005","journal-title":"Numer. Math. J. Chinese Univ."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.01.033"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"R. Metzler and J. Klafter,\n                      The random walk's guide to anomalous diffusion: A fractional dynamics approach\n                      , Phys. Rep., 339 (2000), no. 1.","DOI":"10.1016\/S0370-1573(00)00070-3"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1002\/num.20324"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.02.015"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.05.015"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903433819"},{"key":"R19","unstructured":"I. Podlubny,\n                      Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications\n                      , Math. Sci. Engrg. 198, Academic Press, San Diego, 1999."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.12.033"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.04.025"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(00)00255-7"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-006-9042-x"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100783042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:17:36Z","timestamp":1787325456000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100783042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":23,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100783042"],"URL":"https:\/\/doi.org\/10.1137\/100783042","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}