{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:08:18Z","timestamp":1772294898740,"version":"3.50.1"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/100000163","name":"ARC","doi-asserted-by":"publisher","award":["FT100100172"],"award-info":[{"award-number":["FT100100172"]}],"id":[{"id":"10.13039\/100000163","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11101344"],"award-info":[{"award-number":["11101344"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Fujian","award":["2013J01021"],"award-info":[{"award-number":["2013J01021"]}]},{"name":"Central Universities","award":["2012121001"],"award-info":[{"award-number":["2012121001"]}]},{"name":"Central Universities","award":["2012121002"],"award-info":[{"award-number":["2012121002"]}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1016\/j.amc.2015.01.092","type":"journal-article","created":{"date-parts":[[2015,2,19]],"date-time":"2015-02-19T03:45:33Z","timestamp":1424317533000},"page":"930-938","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":21,"special_numbering":"C","title":["A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation"],"prefix":"10.1016","volume":"256","author":[{"given":"Q.","family":"Liu","sequence":"first","affiliation":[]},{"given":"F.","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Y.T.","family":"Gu","sequence":"additional","affiliation":[]},{"given":"P.","family":"Zhuang","sequence":"additional","affiliation":[]},{"given":"J.","family":"Chen","sequence":"additional","affiliation":[]},{"given":"I.","family":"Turner","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.amc.2015.01.092_b0005","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1023\/A:1010474332598","article-title":"Spectral analysis of fractional kinetic equations with random data","volume":"104","author":"Anh","year":"2001","journal-title":"J. Stat. Phys."},{"issue":"1","key":"10.1016\/j.amc.2015.01.092_b0010","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0096-3003(02)00322-3","article-title":"Harmonic analysis of random fractional diffusion-wave equations. Advanced special functions and related topics in differential equations (Melfi, 2001)","volume":"141","author":"Anh","year":"2003","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.amc.2015.01.092_b0015","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1016\/j.camwa.2009.07.006","article-title":"A new operational matrix for solving fractional-order differential equations","volume":"59","author":"Saadatmandi","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.amc.2015.01.092_b0020","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1016\/j.camwa.2011.04.014","article-title":"A tau approach for solution of the space fractional diffusion equation","volume":"62","author":"Saadatmandi","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.amc.2015.01.092_b0025","doi-asserted-by":"crossref","first-page":"4125","DOI":"10.1016\/j.cnsns.2012.03.003","article-title":"The Sinc\u2013Legendre collocation method for a class of The Sinc\u2013Legendre collocation method for a class of fractional convection-diffusion equation with variable coefficients","volume":"17","author":"Saadatmandi","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"E","key":"10.1016\/j.amc.2015.01.092_b0030","doi-asserted-by":"crossref","first-page":"461","DOI":"10.21914\/anziamj.v45i0.901","article-title":"Numerical solution for the solute transport in fractal porous media","volume":"45","author":"Liu","year":"2004","journal-title":"ANZIAM J."},{"key":"10.1016\/j.amc.2015.01.092_b0035","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.cam.2003.09.028","article-title":"Numerical solution of the space fractional Fokker\u2013Planck equation","volume":"166","author":"Liu","year":"2004","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.amc.2015.01.092_b0040","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.cam.2004.01.033","article-title":"Finite difference approximations for fractional advection\u2013dispersion flow equations","volume":"172","author":"Meerschaert","year":"2004","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.amc.2015.01.092_b0045","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.jcp.2005.05.017","article-title":"Finite difference methods for two-dimensional fractional dispersion equation","volume":"211","author":"Meerschaert","year":"2006","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2015.01.092_b0050","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.jcp.2006.06.005","article-title":"Approximation of the L\u00e9vy\u2013Feller advection\u2013dispersion process by random walk and finite difference method","volume":"222","author":"Liu","year":"2007","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.amc.2015.01.092_b0055","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1137\/060673114","article-title":"New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation","volume":"46","author":"Zhuang","year":"2008","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.01.092_b0060","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1093\/imamat\/hxn044","article-title":"Numerical simulation for the 3D seepage flow with fractional derivatives in porous media","volume":"74","author":"Liu","year":"2009","journal-title":"IMA J. Appl. Math."},{"issue":"1","key":"10.1016\/j.amc.2015.01.092_b0065","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00211-011-0402-3","article-title":"Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials","volume":"120","author":"Sun","year":"2012","journal-title":"Numer. Math."},{"issue":"3","key":"10.1016\/j.amc.2015.01.092_b0070","doi-asserted-by":"crossref","first-page":"463","DOI":"10.2478\/s13540-012-0033-0","article-title":"A product rule for vector fractional derivatives","volume":"15","author":"Bolster","year":"2012","journal-title":"Fract. Calc. Appl. Anal."},{"key":"10.1016\/j.amc.2015.01.092_b0075","doi-asserted-by":"crossref","DOI":"10.1155\/2014\/653797","article-title":"High-order algorithms for Riesz derivative and their applications (I)","author":"Ding","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"10.1016\/j.amc.2015.01.092_b0080","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2014.06.007","article-title":"High-order algorithms for Riesz derivative and their applications (II)","author":"Ding","year":"2014","journal-title":"J. Comput. Phys."},{"issue":"15\u201316","key":"10.1016\/j.amc.2015.01.092_b0085","doi-asserted-by":"crossref","first-page":"3802","DOI":"10.1016\/j.apm.2013.12.002","article-title":"Higher order finite difference method for the reaction and anomalous-diffusion equation","volume":"38","author":"Li","year":"2014","journal-title":"Appl. Math. Model."},{"key":"10.1016\/j.amc.2015.01.092_b0090","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jcp.2012.11.052","article-title":"A high order and unconditionally stable scheme for the modified anomalous fractional subdiffusion equation with a nonlinear source term","volume":"240","author":"Mohebbi","year":"2013","journal-title":"J. Comput. Phys."},{"issue":"10","key":"10.1016\/j.amc.2015.01.092_b0095","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1002\/nme.925","article-title":"Assessment and applications of point interpolation methods for computational mechanics","volume":"59","author":"Liu","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.amc.2015.01.092_b0100","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.cpc.2009.12.010","article-title":"Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)","volume":"181","author":"Dehghan","year":"2010","journal-title":"Comput. Phys. Commun."},{"issue":"5","key":"10.1016\/j.amc.2015.01.092_b0105","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1016\/j.camwa.2009.08.004","article-title":"Fractional diffusion equations by the Kansa method","volume":"59","author":"Chen","year":"2010","journal-title":"Comput. Math. Appl."},{"issue":"3","key":"10.1016\/j.amc.2015.01.092_b0110","first-page":"303","article-title":"An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation","volume":"56","author":"Gu","year":"2010","journal-title":"Comput. Model. Eng. Sci."},{"key":"10.1016\/j.amc.2015.01.092_b0115","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00466-011-0573-x","article-title":"An implicit RBF meshless approach for time fractional diffusion equations","volume":"48","author":"Liu","year":"2010","journal-title":"Comput. Mech."},{"key":"10.1016\/j.amc.2015.01.092_b0120","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1002\/nme.3223","article-title":"Time-dependent fractional advection\u2013diffusion equations by an implicit MLS meshless method","volume":"88","author":"Zhuang","year":"2010","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.amc.2015.01.092_b0125","series-title":"Fractional Differential Equations","author":"Podlubny","year":"1999"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300315001241?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300315001241?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,9,25]],"date-time":"2018-09-25T01:50:25Z","timestamp":1537840225000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300315001241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":25,"alternative-id":["S0096300315001241"],"URL":"https:\/\/doi.org\/10.1016\/j.amc.2015.01.092","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2015,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.amc.2015.01.092","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}