{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:14:56Z","timestamp":1783667696667,"version":"3.55.0"},"reference-count":26,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471373"],"award-info":[{"award-number":["12471373"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117881","type":"journal-article","created":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T04:30:32Z","timestamp":1780720232000},"page":"117881","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations"],"prefix":"10.1016","volume":"489","author":[{"given":"Jingjun","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miaomiao","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6543-5935","authenticated-orcid":false,"given":"Yang","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.cam.2026.117881_bib0001","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.physa.2006.08.071","article-title":"Fractional diffusion models of option prices in markets with jumps","volume":"374","author":"Cartea","year":"2007","journal-title":"Phys. A."},{"key":"10.1016\/j.cam.2026.117881_bib0002","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/S0895-7177(01)00137-6","article-title":"Wave propagation in media with singular memory","volume":"34","author":"Hanyga","year":"2001","journal-title":"Math. Comput. Model."},{"key":"10.1016\/j.cam.2026.117881_bib0003","doi-asserted-by":"crossref","DOI":"10.1088\/1742-5468\/2014\/09\/P09023","article-title":"Tempered fractional time series model for turbulence in geophysical flows","author":"Meerschaert","year":"2014","journal-title":"J. Stat. Mech."},{"key":"10.1016\/j.cam.2026.117881_bib0004","doi-asserted-by":"crossref","DOI":"10.1029\/2008GL034899","article-title":"Tempered anomalous diffusion in heterogeneous systems","volume":"35","author":"Meerschaert","year":"2008","journal-title":"Geophys. Res. Lett."},{"key":"10.1016\/j.cam.2026.117881_bib0005","first-page":"101","article-title":"Essai sur l\u2019\u00e9tude des fonctions, donn\u00e9es par leur d\u00e9veloppement de Taylor","volume":"8","author":"Hadamard","year":"1892","journal-title":"J. Math. Pure. Appl."},{"key":"10.1016\/j.cam.2026.117881_bib0006","doi-asserted-by":"crossref","DOI":"10.1063\/5.0099450","article-title":"Fractional SEIR model and data-driven predictions of COVID-19 dynamics of Omicron variant","volume":"32","author":"Cai","year":"2022","journal-title":"Chaos"},{"key":"10.1016\/j.cam.2026.117881_bib0007","doi-asserted-by":"crossref","first-page":"2903","DOI":"10.1007\/s13540-023-00216-6","article-title":"Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative","volume":"26","author":"Zhao","year":"2023","journal-title":"Fract. Calc. Appl. Anal."},{"key":"10.1016\/j.cam.2026.117881_bib0008","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.apnum.2022.06.013","article-title":"Logarithmic Jacobi collocation method for Caputo-Hadamard fractional differential equations","volume":"181","author":"Zaky","year":"2022","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.cam.2026.117881_bib0009","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2021.106096","article-title":"Numerical approaches to Caputo-Hadamard fractional derivatives with applications to long-term integration of fractional differential systems","volume":"106","author":"Fan","year":"2022","journal-title":"Commun. Nonlinear. Sci."},{"key":"10.1016\/j.cam.2026.117881_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2022.114448","article-title":"A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations","volume":"414","author":"Wang","year":"2022","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117881_bib0011","series-title":"Theory and Numerical Approximations of Fractional Integrals and Derivatives","author":"Li","year":"2020"},{"key":"10.1016\/j.cam.2026.117881_bib0012","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1002\/num.20112","article-title":"Variational formulation for the stationary fractional advection dispersion equation","volume":"22","author":"Ervin","year":"2006","journal-title":"Numer. Meth. Part. Differ. Eq."},{"key":"10.1016\/j.cam.2026.117881_bib0013","series-title":"Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations","author":"Zayernouri","year":"2024"},{"key":"10.1016\/j.cam.2026.117881_bib0014","series-title":"Theory and Applications of Fractional Differential Equations","author":"Kilbas","year":"2006"},{"key":"10.1016\/j.cam.2026.117881_bib0015","doi-asserted-by":"crossref","first-page":"631","DOI":"10.3846\/mma.2021.13252","article-title":"Differential equations with tempered \u03a8-Caputo fractional derivative","volume":"26","author":"Medve\u010f","year":"2021","journal-title":"Math. Model. Anal."},{"key":"10.1016\/j.cam.2026.117881_bib0016","doi-asserted-by":"crossref","first-page":"11134","DOI":"10.1002\/mma.8441","article-title":"On tempered fractional calculus with respect to functions and the associated fractional differential equations","volume":"45","author":"Mali","year":"2022","journal-title":"Math. Method. Appl. Sci."},{"key":"10.1016\/j.cam.2026.117881_bib0017","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1186\/1687-1847-2012-142","article-title":"Caputo-type modification of the Hadamard fractional derivatives","volume":"2012","author":"Jarad","year":"2012","journal-title":"Adv. Differ. Equ."},{"key":"10.1016\/j.cam.2026.117881_bib0018","doi-asserted-by":"crossref","first-page":"A701","DOI":"10.1137\/140980545","article-title":"A novel high order space-time spectral method for the time fractional Fokker-Planck equation","volume":"37","author":"Zheng","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2026.117881_bib0019","doi-asserted-by":"crossref","first-page":"2108","DOI":"10.1137\/080718942","article-title":"A space-time spectral method for the time fractional diffusion equation","volume":"47","author":"Li","year":"2009","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117881_bib0020","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.jcp.2013.06.031","article-title":"Fractional Sturm-Liouville eigen-problems: theory numerical approximation","volume":"252","author":"Zayernouri","year":"2013","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.cam.2026.117881_bib0021","doi-asserted-by":"crossref","first-page":"A1003","DOI":"10.1137\/16M1073121","article-title":"Petrov-Galerkin and spectral collocation methods for distributed order differential equations","volume":"39","author":"Kharazmi","year":"2017","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2026.117881_bib0022","doi-asserted-by":"crossref","first-page":"A1777","DOI":"10.1137\/140985536","article-title":"Tempered fractional Sturm-Liouville eigenproblems","volume":"37","author":"Zayernouri","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2026.117881_bib0023","series-title":"Problems and Solutions in Introductory and Advanced Matrix Calculus","author":"Steeb","year":"2006"},{"key":"10.1016\/j.cam.2026.117881_bib0024","first-page":"302","article-title":"A time-space spectral method for the time-space fractional Fokker-Planck equation and its inverse problem","volume":"320","author":"Zhang","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117881_bib0025","first-page":"209","article-title":"Spectral methods","volume":"5","author":"Bernardi","year":"1997","journal-title":"Numer. Anal."},{"key":"10.1016\/j.cam.2026.117881_bib0026","series-title":"Non-homogeneous Boundary Value Problems and Applications, Vol. I","author":"Lions","year":"1972"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005236?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005236?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:44:40Z","timestamp":1783665880000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":26,"alternative-id":["S0377042726005236"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117881","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A Petrov-Galerkin spectral method for tempered Caputo-Hadamard fractional diffusion equations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117881","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117881"}}