{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T11:19:06Z","timestamp":1773141546413,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T00:00:00Z","timestamp":1610928000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T00:00:00Z","timestamp":1610928000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,2]]},"DOI":"10.1007\/s40314-020-01410-5","type":"journal-article","created":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T16:06:36Z","timestamp":1610985996000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Numerical treatment of the space fractional advection\u2013dispersion model arising in groundwater hydrology"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7002-5922","authenticated-orcid":false,"given":"H.","family":"Mesgarani","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9177-900X","authenticated-orcid":false,"given":"J.","family":"Rashidinia","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5109-1561","authenticated-orcid":false,"given":"Y. Esmaeelzade","family":"Aghdam","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"O.","family":"Nikan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,18]]},"reference":[{"key":"1410_CR1","doi-asserted-by":"publisher","unstructured":"Aghdam YE, Mesgrani H, Javidi M, Nikan O (2020) A computational approach for the space-time fractional advection-diffusion equation arising in contaminant transport through porous media. Eng Comput. https:\/\/doi.org\/10.1007\/s00366-020-01021-y","DOI":"10.1007\/s00366-020-01021-y"},{"key":"1410_CR2","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.ijthermalsci.2015.06.013","volume":"97","author":"L Colla","year":"2015","unstructured":"Colla L, Fedele L, Buschmann M (2015) Laminar mixed convection of TiO2-water nanofluid in horizontal uniformly heated pipe flow. Int J Therm Sci 97:26\u201340","journal-title":"Int J Therm Sci"},{"issue":"2","key":"1410_CR3","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1002\/num.20169","volume":"23","author":"VJ Ervin","year":"2007","unstructured":"Ervin VJ, Roop JP (2007) Variational solution of fractional advection dispersion equations on bounded domains in 1d. Numer Methods Partial Differ Equ Int J 23(2):256\u2013281","journal-title":"Numer Methods Partial Differ Equ Int J"},{"issue":"2","key":"1410_CR4","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1137\/050642757","volume":"45","author":"VJ Ervin","year":"2007","unstructured":"Ervin VJ, Heuer N, Roop JP (2007) Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation. SIAM J Numer Anal 45(2):572\u2013591","journal-title":"SIAM J Numer Anal"},{"key":"1410_CR5","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.cemconcomp.2015.03.006","volume":"59","author":"A Farahani","year":"2015","unstructured":"Farahani A, Taghaddos H, Shekarchi M (2015) Prediction of long-term chloride diffusion in silica fume concrete in a marine environment. Cement Con Compos 59:10\u201317","journal-title":"Cement Con Compos"},{"issue":"4","key":"1410_CR6","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s40314-019-0957-7","volume":"38","author":"A Golbabai","year":"2019","unstructured":"Golbabai A, Nikan O, Nikazad T (2019a) Numerical analysis of time fractional Black\u2013Scholes European option pricing model arising in financial market. Comput Appl Math 38(4):173","journal-title":"Comput Appl Math"},{"issue":"3","key":"1410_CR7","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s40819-019-0635-x","volume":"5","author":"A Golbabai","year":"2019","unstructured":"Golbabai A, Nikan O, Nikazad T (2019b) Numerical investigation of the time fractional mobile-immobile advection-dispersion model arising from solute transport in porous media. Int J Appl Comput Math 5(3):50","journal-title":"Int J Appl Comput Math"},{"issue":"1\u20132","key":"1410_CR8","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/0010-2180(94)00182-R","volume":"101","author":"J Hernandez","year":"1995","unstructured":"Hernandez J, Crespo A, Duijm N (1995) Numerical modeling of turbulent jet diffusion flames in the atmospheric surface layer. Combust flame 101(1\u20132):113\u2013131","journal-title":"Combust flame"},{"key":"1410_CR9","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1016\/j.ijheatmasstransfer.2015.11.078","volume":"95","author":"G Hu","year":"2016","unstructured":"Hu G, Zhao L, Wu X, Li R, Wu T, Xie C, Qiao Y, Shi J, Li W, Cheng G (2016) New Fourier-series-based analytical solution to the conduction\u2013convection equation to calculate soil temperature, determine soil thermal properties, or estimate water flux. Int J Heat Mass Transfer 95:815\u2013823","journal-title":"Int J Heat Mass Transfer"},{"issue":"3","key":"1410_CR10","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1007\/s40314-013-0091-x","volume":"33","author":"M Khader","year":"2014","unstructured":"Khader M, Sweilam N (2014) Approximate solutions for the fractional advection-dispersion equation using legendre pseudo-spectral method. Comput Appl Math 33(3):739\u2013750","journal-title":"Comput Appl Math"},{"issue":"1","key":"1410_CR11","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.cam.2003.09.028","volume":"166","author":"F Liu","year":"2004","unstructured":"Liu F, Anh V, Turner I (2004) Numerical solution of the space fractional Fokker\u2013Planck equation. J Comput Appl Math 166(1):209\u2013219","journal-title":"J Comput Appl Math"},{"key":"1410_CR12","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.cnsns.2016.02.009","volume":"38","author":"L Liu","year":"2016","unstructured":"Liu L, Zheng L, Liu F, Zhang X (2016) Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo\u2013Christov flux. Commun Nonlinear Sci Numer Simul 38:45\u201358","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"6","key":"1410_CR13","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s40819-019-0737-5","volume":"5","author":"M Mahmoudi","year":"2019","unstructured":"Mahmoudi M, Ghovatmand M, Jafari H (2019) An adaptive collocation method for solving delay fractional differential equations. Int J Appl Comput Math 5(6):157","journal-title":"Int J Appl Comput Math"},{"key":"1410_CR14","volume-title":"Introduction to fractional differential equations","author":"C Milici","year":"2018","unstructured":"Milici C, Dr\u0103g\u0103nescu G, Machado JT (2018) Introduction to fractional differential equations, vol 25. Springer, Berlin"},{"key":"1410_CR15","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1016\/j.apm.2020.07.021","volume":"89","author":"O Nikan","year":"2020","unstructured":"Nikan O, Machado JT, Golbabai A (2020) Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments. Appl Math Model 89:819\u2013836","journal-title":"Appl Math Model"},{"key":"1410_CR16","unstructured":"Oldham KB, Spanier J (1974) The fractional calculus, vol. 111 of Mathematics in science and engineering"},{"key":"1410_CR17","doi-asserted-by":"publisher","first-page":"105022","DOI":"10.1016\/j.cnsns.2019.105022","volume":"82","author":"MD Ortigueira","year":"2020","unstructured":"Ortigueira MD, Machado JT (2020) On the properties of some operators under the perspective of fractional system theory. Commun Nonlinear Sci Numer Simul 82:105022","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"1410_CR18","volume-title":"Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications,","author":"I Podlubny","year":"1998","unstructured":"Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol 198. Elsevier, Amsterdam"},{"issue":"5","key":"1410_CR19","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1007\/s40819-019-0720-1","volume":"5","author":"F Rigi","year":"2019","unstructured":"Rigi F, Tajadodi H (2019) Numerical approach of fractional Abel differential equation by Genocchi polynomials. Int J Appl Comput Math 5(5):134","journal-title":"Int J Appl Comput Math"},{"issue":"2","key":"1410_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40314-020-1078-z","volume":"39","author":"H Safdari","year":"2020","unstructured":"Safdari H, Mesgarani H, Javidi M, Aghdam YE (2020b) Convergence analysis of the space fractional-order diffusion equation based on the compact finite difference scheme. Comput Appl Math 39(2):1\u201315","journal-title":"Comput Appl Math"},{"key":"1410_CR21","doi-asserted-by":"publisher","unstructured":"Safdari H, Aghdam YE, G\u00f3mez-Aguilar J (2020a) Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space-time fractional advection\u2013diffusion equation. Eng Comput. https:\/\/doi.org\/10.1007\/s00366-020-01092-x","DOI":"10.1007\/s00366-020-01092-x"},{"issue":"3","key":"1410_CR22","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/s40819-018-0517-7","volume":"4","author":"V Saw","year":"2018","unstructured":"Saw V, Kumar S (2018) Fourth kind shifted Chebyshev polynomials for solving space fractional order advection-dispersion equation based on collocation method and finite difference approximation. Int J Appl Comput Math 4(3):82","journal-title":"Int J Appl Comput Math"},{"issue":"3","key":"1410_CR23","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1007\/s40995-018-0480-5","volume":"43","author":"V Saw","year":"2019","unstructured":"Saw V, Kumar S (2019) Second kind Chebyshev polynomials for solving space fractional advection-dispersion equation using collocation method. Iran J Sci Technol Trans A Sci 43(3):1027\u20131037","journal-title":"Iran J Sci Technol Trans A Sci"},{"issue":"11","key":"1410_CR24","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1016\/j.amc.2010.04.060","volume":"216","author":"L Su","year":"2010","unstructured":"Su L, Wang W, Xu Q (2010) Finite difference methods for fractional dispersion equations. Appl Math Comput 216(11):3329\u20133334","journal-title":"Appl Math Comput"},{"key":"1410_CR25","unstructured":"Tenreiro\u00a0Machado JA, Lopes AM (2019) Fractional-order kinematic analysis of biomechanical inspired manipulators. J Vibrat Control: 102\u2013111"},{"issue":"4","key":"1410_CR26","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/s40314-019-0944-z","volume":"38","author":"S Toubaei","year":"2019","unstructured":"Toubaei S, Garshasbi M, Reihani P (2019) Boundary functions determination in an inverse time fractional heat conduction problem. Comput Appl Math 38(4):190","journal-title":"Comput Appl Math"},{"issue":"3","key":"1410_CR27","doi-asserted-by":"publisher","first-page":"1268","DOI":"10.1016\/j.jfranklin.2013.10.011","volume":"351","author":"A Zaib","year":"2014","unstructured":"Zaib A, Shafie S (2014) Thermal diffusion and diffusion thermo effects on unsteady mhd free convection flow over a stretching surface considering joule heating and viscous dissipation with thermal stratification, chemical reaction and hall current. J Franklin Inst 351(3):1268\u20131287","journal-title":"J Franklin Inst"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01410-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-020-01410-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01410-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T20:25:40Z","timestamp":1613075140000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-020-01410-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,18]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["1410"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01410-5","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,18]]},"assertion":[{"value":"24 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"22"}}