{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T13:05:09Z","timestamp":1784898309236,"version":"3.55.0"},"reference-count":34,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung Technologie und Raumfahrt Informationstechnikzentrum Bund","doi-asserted-by":"publisher","award":["05M22WHA"],"award-info":[{"award-number":["05M22WHA"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.matcom.2026.05.007","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T09:29:44Z","timestamp":1778750984000},"page":"18-38","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["An efficient exponential sum approximation of power-law kernels for solving fractional differential equations"],"prefix":"10.1016","volume":"249","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3721-3395","authenticated-orcid":false,"given":"Renu","family":"Chaudhary","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Diethelm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Afshin","family":"Farhadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fred A.","family":"Fuchs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.05.007_b1","series-title":"Fractional Calculus\u2014Models and Numerical Methods","author":"Baleanu","year":"2016"},{"key":"10.1016\/j.matcom.2026.05.007_b2","series-title":"HandBook of Fractional Calculus with Applications, 7: Applications in Engineering, Life and Social Sciences, Part a","year":"2019"},{"key":"10.1016\/j.matcom.2026.05.007_b3","series-title":"HandBook of Fractional Calculus with Applications, 8: Applications in Engineering, Life and Social Sciences, Part B","year":"2019"},{"key":"10.1016\/j.matcom.2026.05.007_b4","series-title":"Fractional Differential Equations","author":"Diethelm","year":"2010"},{"key":"10.1016\/j.matcom.2026.05.007_b5","series-title":"HandBook of Fractional Calculus with Applications, 6: Applications in Control","year":"2019"},{"key":"10.1016\/j.matcom.2026.05.007_b6","series-title":"HandBook of Fractional Calculus with Applications, 4: Applications in Physics, Part a","year":"2019"},{"key":"10.1016\/j.matcom.2026.05.007_b7","series-title":"HandBook of Fractional Calculus with Applications, 5: Applications in Physics, Part B","year":"2019"},{"key":"10.1016\/j.matcom.2026.05.007_b8","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10915-018-0848-x","article-title":"A Gauss-Jacobi kernel compression scheme for fractional differential equations","volume":"79","author":"Baffet","year":"2019","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.matcom.2026.05.007_b9","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1137\/15M1043960","article-title":"A kernel compression scheme for fractional differential equations","volume":"55","author":"Baffet","year":"2017","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.matcom.2026.05.007_b10","doi-asserted-by":"crossref","first-page":"4696","DOI":"10.1137\/080736533","article-title":"A fast time stepping method for evaluating fractional integrals","volume":"31","author":"Li","year":"2010","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.matcom.2026.05.007_b11","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.acha.2005.01.003","article-title":"On approximation of functions by exponential sums","volume":"19","author":"Beylkin","year":"2005","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"10.1016\/j.matcom.2026.05.007_b12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.acha.2009.08.011","article-title":"Approximation by exponential sums revisited","volume":"28","author":"Beylkin","year":"2010","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"10.1016\/j.matcom.2026.05.007_b13","series-title":"Contemporary Computational Mathematics","first-page":"911","article-title":"Exponential sum approximations for t\u2212\u03b2","author":"McLean","year":"2018"},{"key":"10.1016\/j.matcom.2026.05.007_b14","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1090\/S0025-5718-1985-0804935-7","article-title":"Fractional linear multistep methods for abel-volterra integral equations of the second kind","volume":"45","author":"Lubich","year":"1985","journal-title":"Math. Comp."},{"key":"10.1016\/j.matcom.2026.05.007_b15","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1137\/0517050","article-title":"Discretized fractional calculus","volume":"17","author":"Lubich","year":"1986","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/j.matcom.2026.05.007_b16","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1016592219341","article-title":"A predictor\u2013corrector approach for the numerical solution of fractional differential equations","volume":"29","author":"Diethelm","year":"2002","journal-title":"Nonlinear Dynam."},{"key":"10.1016\/j.matcom.2026.05.007_b17","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1023\/B:NUMA.0000027736.85078.be","article-title":"Detailed error analysis for a fractional Adams method","volume":"36","author":"Diethelm","year":"2004","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.matcom.2026.05.007_b18","doi-asserted-by":"crossref","first-page":"16","DOI":"10.3390\/math6020016","article-title":"Numerical solution of fractional differential equations: A survey and a software tutorial","volume":"6","author":"Garrappa","year":"2018","journal-title":"Mathematics"},{"key":"10.1016\/j.matcom.2026.05.007_b19","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1137\/0906037","article-title":"Fast numerical solution of nonlinear volterra convolution equations","volume":"6","author":"Hairer","year":"1985","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"10.1016\/j.matcom.2026.05.007_b20","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0377-0427(88)90332-9","article-title":"Fast numerical solution of weakly singular volterra integral equations","volume":"23","author":"Hairer","year":"1988","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.matcom.2026.05.007_b21","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.camwa.2005.07.010","article-title":"An efficient algorithm for the evaluation of convolution integrals","volume":"51","author":"Diethelm","year":"2006","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.matcom.2026.05.007_b22","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1023\/A:1016601312158","article-title":"The numerical solution of fractional differential equations: speed versus accuracy","volume":"26","author":"Ford","year":"2001","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.matcom.2026.05.007_b23","series-title":"INdAM Workshop on Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers","first-page":"1","article-title":"A new diffusive representation for fractional derivatives, part I: construction, implementation and numerical examples","author":"Diethelm","year":"2021"},{"key":"10.1016\/j.matcom.2026.05.007_b24","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.3390\/math10081245","article-title":"A new diffusive representation for fractional derivatives, part ii: Convergence analysis of the numerical scheme","volume":"10","author":"Diethelm","year":"2022","journal-title":"Mathematics"},{"key":"10.1016\/j.matcom.2026.05.007_b25","first-page":"412","article-title":"Novel variants of diffusive representation of fractional integrals: Construction and numerical computation","volume":"58","author":"Chaudhary","year":"2024","journal-title":"IFAC Pap."},{"key":"10.1016\/j.matcom.2026.05.007_b26","first-page":"418","article-title":"Revisiting diffusive representations for enhanced numerical approximation of fractional integrals","volume":"58","author":"Chaudhary","year":"2024","journal-title":"IFAC Pap."},{"key":"10.1016\/j.matcom.2026.05.007_b27","unstructured":"NIST Digital Library of Mathematical Functions. https:\/\/dlmf.nist.gov\/, Release 1.2.4 of 2025-03-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds."},{"key":"10.1016\/j.matcom.2026.05.007_b28","unstructured":"R. Prony, Essai exp\u00e9rimental et analytique, J. L\u2019\u00c9cole Polytech. 1 (1795) 24\u201376."},{"key":"10.1016\/j.matcom.2026.05.007_b29","article-title":"Prony\u2019s method: an old trick for new problems","volume":"4","author":"Sauer","year":"2018","journal-title":"Snapshots Mod. Math. from Oberwolfach"},{"key":"10.1016\/j.matcom.2026.05.007_b30","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1186\/s12859-018-2473-y","article-title":"Coding prony\u2019s method in matlab and applying it to biomedical signal filtering","volume":"19","author":"Fern\u00e1ndez Rodr\u00edguez","year":"2018","journal-title":"BMC Bioinformatics"},{"key":"10.1016\/j.matcom.2026.05.007_b31","series-title":"The Gamma Function","author":"Artin","year":"2015"},{"key":"10.1016\/j.matcom.2026.05.007_b32","series-title":"Concise Numerical Mathematics","author":"Plato","year":"2003"},{"key":"10.1016\/j.matcom.2026.05.007_b33","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1137\/140971191","article-title":"Numerical evaluation of two and three parameter Mittag-Leffler functions","volume":"53","author":"Garrappa","year":"2015","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.matcom.2026.05.007_b34","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.mechrescom.2005.02.018","article-title":"On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems","volume":"33","author":"Schmidt","year":"2006","journal-title":"Mech. Res. Commun."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002041?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002041?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T12:40:09Z","timestamp":1784896809000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426002041"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":34,"alternative-id":["S0378475426002041"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.05.007","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"An efficient exponential sum approximation of power-law kernels for solving fractional differential equations","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.05.007","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).","name":"copyright","label":"Copyright"}]}}