{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:16:50Z","timestamp":1778707010859,"version":"3.51.4"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T00:00:00Z","timestamp":1778630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"UG","award":["191620007868."],"award-info":[{"award-number":["191620007868."]}]},{"name":"SER","award":["CRG\/2022\/000813"],"award-info":[{"award-number":["CRG\/2022\/000813"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1007\/s40314-026-03792-4","type":"journal-article","created":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T08:17:42Z","timestamp":1778660262000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation of Caputo derivative by using product integration techniques and its application"],"prefix":"10.1007","volume":"45","author":[{"given":"Sunil","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shivani","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subir","family":"Das","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vineet Kumar","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,13]]},"reference":[{"issue":"11","key":"3792_CR1","doi-asserted-by":"publisher","first-page":"12743","DOI":"10.3934\/math.2021735","volume":"6","author":"RB Albadarneh","year":"2021","unstructured":"Albadarneh RB, Batiha I, Alomari A, Tahat N (2021) Numerical approach for approximating the Caputo fractional-order derivative operator. AIMS Math 6(11):12743\u201312756","journal-title":"AIMS Math"},{"key":"3792_CR2","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.jcp.2014.09.031","volume":"280","author":"AA Alikhanov","year":"2015","unstructured":"Alikhanov AA (2015) A new difference scheme for the time fractional diffusion equation. J Comput Phys 280:424\u2013438","journal-title":"J Comput Phys"},{"key":"3792_CR3","volume":"411","author":"AA Alikhanov","year":"2021","unstructured":"Alikhanov AA, Huang C (2021) A high-order L2 type difference scheme for the time-fractional diffusion equation. Appl Math Comput 411:126545","journal-title":"Appl Math Comput"},{"key":"3792_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinam.2022.100258","volume":"14","author":"M Alshbool","year":"2022","unstructured":"Alshbool M, Mohammad M, Isik O, Hashim I (2022) Fractional Bernstein operational matrices for solving integro-differential equations involved by Caputo fractional derivative. Results Appl Math 14:100258","journal-title":"Results Appl Math"},{"issue":"2","key":"3792_CR5","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1017\/S0020268100012294","volume":"73","author":"R Beard","year":"1947","unstructured":"Beard R (1947) Some notes on approximate product-integration. J Inst Act 73(2):356\u2013416","journal-title":"J Inst Act"},{"issue":"11","key":"3792_CR6","doi-asserted-by":"publisher","first-page":"9419","DOI":"10.1002\/mma.7369","volume":"44","author":"P Das","year":"2021","unstructured":"Das P, Rana S (2021) Theoretical prospects of fractional order weakly singular Volterra integro differential equations and their approximations with convergence analysis. Math Methods Appl Sci 44(11):9419\u20139440","journal-title":"Math Methods Appl Sci"},{"key":"3792_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2020.113116","volume":"404","author":"P Das","year":"2022","unstructured":"Das P, Rana S, Ramos H (2022) On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and their convergence analysis. J Comput Appl Math 404:113116","journal-title":"J Comput Appl Math"},{"key":"3792_CR8","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1016\/j.jcp.2018.10.011","volume":"376","author":"R Du","year":"2019","unstructured":"Du R, Yan Y, Liang Z (2019) A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation. J Comput Phys 376:1312\u20131330","journal-title":"J Comput Phys"},{"issue":"11","key":"3792_CR9","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.3390\/math13111793","volume":"13","author":"KT Elgindy","year":"2025","unstructured":"Elgindy KT (2025) The numerical approximation of Caputo fractional derivatives of higher orders using a Shifted Gegenbauer Pseudospectral method: a case study of two-point boundary value problems of the Bagley-Torvik type. Mathematics 13(11):1793","journal-title":"Mathematics"},{"key":"3792_CR10","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.jcp.2013.11.017","volume":"259","author":"G-H Gao","year":"2014","unstructured":"Gao G-H, Sun Z-Z, Zhang H-W (2014) A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications. J Comput Phys 259:33\u201350","journal-title":"J Comput Phys"},{"issue":"5","key":"3792_CR11","doi-asserted-by":"publisher","first-page":"7271","DOI":"10.1007\/s12190-025-02567-0","volume":"71","author":"A Ghoreyshi","year":"2025","unstructured":"Ghoreyshi A, Abbaszadeh M, Zaky MA, Dehghan M (2025) Two high-order numerical schemes based on the Lagrange polynomials for solving a distributed-order time-fractional partial integro-differential equation on non-rectangular domains. J Appl Math Comput 71(5):7271\u20137311","journal-title":"J Appl Math Comput"},{"issue":"13","key":"3792_CR12","first-page":"4385","volume":"7","author":"J Jacob","year":"2020","unstructured":"Jacob J, Priya J, Karthika A (2020) Applications of fractional calculus in science and engineering. J Crit Rev 7(13):4385\u20134394","journal-title":"J Crit Rev"},{"issue":"3","key":"3792_CR13","doi-asserted-by":"publisher","first-page":"650","DOI":"10.4208\/cicp.OA-2016-0136","volume":"21","author":"S Jiang","year":"2017","unstructured":"Jiang S, Zhang J, Zhang Q, Zhang Z (2017) Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun Comput Phys 21(3):650\u2013678","journal-title":"Commun Comput Phys"},{"key":"3792_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.bspc.2013.08.006","volume":"9","author":"V Joshi","year":"2014","unstructured":"Joshi V, Pachori RB, Vijesh A (2014) Classification of ictal and seizure-free EEG signals using fractional linear prediction. Biomed Signal Process 9:1\u20135","journal-title":"Biomed Signal Process"},{"key":"3792_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(06)80001-0","volume-title":"Theory and applications of fractional differential equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations, vol 204. Elsevier, Amsterdam"},{"key":"3792_CR16","volume-title":"Generalized fractional calculus and applications","author":"VS Kiryakova","year":"1993","unstructured":"Kiryakova VS (1993) Generalized fractional calculus and applications. CRC Press, Boca Raton"},{"issue":"3","key":"3792_CR17","doi-asserted-by":"publisher","first-page":"2833","DOI":"10.1002\/mma.10464","volume":"48","author":"S Kumar","year":"2025","unstructured":"Kumar S, Yadav P, Kumar Singh V (2025) Product integration techniques for fractional integro-differential equations. Math Methods Appl Sci 48(3):2833\u20132858","journal-title":"Math Methods Appl Sci"},{"issue":"2","key":"3792_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00033-025-02451-8","volume":"76","author":"S Kumar","year":"2025","unstructured":"Kumar S, Das S, Singh VK (2025) Product integration techniques for generalized fractional integro-differential equations. Z Angew Math Phys 76(2):1\u201330","journal-title":"Z Angew Math Phys"},{"issue":"1","key":"3792_CR19","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0898-1221(98)00109-6","volume":"36","author":"J Li","year":"1998","unstructured":"Li J (1998) Global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem. Comput Math Appl 36(1):59\u201367","journal-title":"Comput Math Appl"},{"issue":"2","key":"3792_CR20","first-page":"777","volume":"187","author":"C Li","year":"2007","unstructured":"Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777\u2013784","journal-title":"Appl Math Comput"},{"issue":"2","key":"3792_CR21","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1515\/ijnsns-2021-0189","volume":"24","author":"C Li","year":"2023","unstructured":"Li C, Li Z (2023) Stability and $$\\psi $$-algebraic decay of the solution to $$\\psi $$-fractional differential system. Int J Nonlinear Sci Numer Simul 24(2):695\u2013733","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"3792_CR22","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.cam.2015.11.037","volume":"299","author":"H Li","year":"2016","unstructured":"Li H, Cao J, Li C (2016) High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (iii). J Comput Appl Math 299:159\u2013175","journal-title":"J Comput Appl Math"},{"issue":"2","key":"3792_CR23","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1016\/j.jcp.2007.02.001","volume":"225","author":"Y Lin","year":"2007","unstructured":"Lin Y, Xu C (2007) Finite difference\/spectral approximations for the time-fractional diffusion equation. J Comput Phys 225(2):1533\u20131552","journal-title":"J Comput Phys"},{"issue":"1","key":"3792_CR24","doi-asserted-by":"publisher","first-page":"C164","DOI":"10.1137\/25M1748895","volume":"48","author":"Z Lin","year":"2026","unstructured":"Lin Z, Ma Q, Xie H, Yin X (2026) Solving time-fractional partial integro-differential equations using tensor neural network. SIAM J Sci Comput 48(1):C164\u2013C189","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"3792_CR25","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-Planck equation. J Comput Appl Math 166(1):209\u2013219","journal-title":"J Comput Appl Math"},{"key":"3792_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112395","volume":"161","author":"Z Luo","year":"2022","unstructured":"Luo Z, Zhang X, Wang S, Yao L (2022) Numerical approximation of time fractional partial integro-differential equation based on compact finite difference scheme. Chaos Solit Fract 161:112395","journal-title":"Chaos Solit Fract"},{"issue":"12","key":"3792_CR27","first-page":"6750","volume":"219","author":"X Ma","year":"2013","unstructured":"Ma X, Huang C (2013) Numerical solution of fractional integro-differential equations by a hybrid collocation method. Appl Math Comput 219(12):6750\u20136760","journal-title":"Appl Math Comput"},{"issue":"3","key":"3792_CR28","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1016\/j.cnsns.2010.05.027","volume":"16","author":"JT Machado","year":"2011","unstructured":"Machado JT, Kiryakova V, Mainardi F (2011) Recent history of fractional calculus. Commun Nonlinear Sci Numer Simul 16(3):1140\u20131153","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3792_CR29","doi-asserted-by":"crossref","unstructured":"Magin R (2004) Fractional calculus in bioengineering, part 1. Crit $$\\text{Rev}^{{\\rm TM}}$$ Biomed Eng 32(1)","DOI":"10.1615\/CritRevBiomedEng.v32.10"},{"key":"3792_CR30","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.matcom.2023.09.013","volume":"216","author":"I Masti","year":"2024","unstructured":"Masti I, Sayevand K (2024) On collocation-Galerkin method and fractional B-spline functions for a class of stochastic fractional integro-differential equations. Math Comput Simul 216:263\u2013287","journal-title":"Math Comput Simul"},{"issue":"1","key":"3792_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42967-019-00023-y","volume":"2","author":"R Mokhtari","year":"2020","unstructured":"Mokhtari R, Mostajeran F (2020) A high order formula to approximate the Caputo fractional derivative. Commun Appl Math Comput 2(1):1\u201329","journal-title":"Commun Appl Math Comput"},{"issue":"1","key":"3792_CR32","first-page":"754","volume":"182","author":"S Momani","year":"2006","unstructured":"Momani S, Noor MA (2006) Numerical methods for fourth-order fractional integro-differential equations. Appl Math Comput 182(1):754\u2013760","journal-title":"Appl Math Comput"},{"issue":"2","key":"3792_CR33","first-page":"527","volume":"178","author":"Z Odibat","year":"2006","unstructured":"Odibat Z (2006) Approximations of fractional integrals and Caputo fractional derivatives. Appl Math Comput 178(2):527\u2013533","journal-title":"Appl Math Comput"},{"key":"3792_CR34","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,"},{"key":"3792_CR35","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.matcom.2024.02.005","volume":"221","author":"MAP Pulido","year":"2024","unstructured":"Pulido MAP, Sousa JVC, De Oliveira EC (2024) New discretization of $$\\psi $$-Caputo fractional derivative and applications. Math Comput Simul 221:135\u2013158","journal-title":"Math Comput Simul"},{"issue":"5","key":"3792_CR36","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10409-007-0093-2","volume":"23","author":"H Qi","year":"2007","unstructured":"Qi H, Xu M (2007) Stokes first problem for a viscoelastic fluid with the generalized Oldroyd-B model. Acta Mech Sin 23(5):463\u2013469","journal-title":"Acta Mech Sin"},{"issue":"1","key":"3792_CR37","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.asej.2019.08.004","volume":"11","author":"N Rajagopal","year":"2020","unstructured":"Rajagopal N, Balaji S, Seethalakshmi R, Balaji V (2020) A new numerical method for fractional order Volterra integro-differential equations. Ain Shams Eng J 11(1):171\u2013177","journal-title":"Ain Shams Eng J"},{"key":"3792_CR38","volume-title":"Fractional integrals and derivatives: theory and applications","author":"SG Samko","year":"1993","unstructured":"Samko SG (1993) Fractional integrals and derivatives: theory and applications. Gordon and Breach, Basel"},{"issue":"4","key":"3792_CR39","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1007\/s11075-024-01927-4","volume":"99","author":"S Santra","year":"2025","unstructured":"Santra S (2025) Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels. Numer Algorithms 99(4):1649\u20131695","journal-title":"Numer Algorithms"},{"issue":"11","key":"3792_CR40","doi-asserted-by":"publisher","first-page":"6677","DOI":"10.1002\/mma.8199","volume":"45","author":"S Santra","year":"2022","unstructured":"Santra S, Mohapatra J (2022) Analysis of a finite difference method based on L1 discretization for solving multi-term fractional differential equation involving weak singularity. Math Methods Appl Sci 45(11):6677\u20136690","journal-title":"Math Methods Appl Sci"},{"key":"3792_CR41","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.camwa.2023.09.008","volume":"150","author":"S Santra","year":"2023","unstructured":"Santra S, Mohapatra J, Das P, Choudhuri D (2023) Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis. Comput Math Appl 150:87\u2013101","journal-title":"Comput Math Appl"},{"key":"3792_CR42","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1007\/s40819-017-0428-z","volume":"3","author":"K Sayevand","year":"2017","unstructured":"Sayevand K, Jafarian H (2017) Solving integro-differential equation with an integral boundary condition using the Reproducing Kernel. Int J Appl Comput Math 3:1425\u20131433","journal-title":"Int J Appl Comput Math"},{"issue":"17","key":"3792_CR43","doi-asserted-by":"publisher","first-page":"9928","DOI":"10.1002\/mma.6667","volume":"43","author":"K Sayevand","year":"2020","unstructured":"Sayevand K, Tenreiro Machado J, Masti I (2020) On dual Bernstein polynomials and stochastic fractional integro-differential equations. Math Meth Appl Sci 43(17):9928\u20139947","journal-title":"Math Meth Appl Sci"},{"issue":"2","key":"3792_CR44","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1007\/s10915-020-01219-8","volume":"83","author":"J Shen","year":"2020","unstructured":"Shen J, Li C, Sun Z-Z (2020) An H2N2 interpolation for Caputo derivative with order in (1, 2) and its application to time-fractional wave equations in more than one space dimension. J Sci Comput 83(2):38","journal-title":"J Sci Comput"},{"issue":"2","key":"3792_CR45","first-page":"276","volume":"7","author":"E Shivanian","year":"2019","unstructured":"Shivanian E, Fatahi H (2019) Analysis of meshless local radial point interpolant on a model in population dynamics. Comput Methods Differ Equ 7(2):276\u2013288","journal-title":"Comput Methods Differ Equ"},{"issue":"7","key":"3792_CR46","doi-asserted-by":"publisher","first-page":"896","DOI":"10.1002\/fld.5077","volume":"94","author":"D Singh","year":"2022","unstructured":"Singh D, Sultana F, Pandey RK (2022) Approximation of Caputo-Prabhakar derivative with application in solving time fractional advection-diffusion equation. Int J Numer Meth Fluids 94(7):896\u2013919","journal-title":"Int J Numer Meth Fluids"},{"key":"3792_CR47","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1016\/j.matcom.2022.10.003","volume":"205","author":"N Srivastava","year":"2023","unstructured":"Srivastava N, Singh VK (2023) L3 approximation of Caputo derivative and its application to time-fractional wave equation-(i). Math Comput Simul 205:532\u2013557","journal-title":"Math Comput Simul"},{"issue":"5","key":"3792_CR48","doi-asserted-by":"publisher","first-page":"269","DOI":"10.3390\/fractalfract9050269","volume":"9","author":"P Stempin","year":"2025","unstructured":"Stempin P, Sumelka W (2025) Approximation of fractional Caputo derivative of variable order and variable terminals with application to initial\/boundary value problems. Fractal Fract 9(5):269","journal-title":"Fractal Fract"},{"issue":"2","key":"3792_CR49","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1137\/16M1082329","volume":"55","author":"M Stynes","year":"2017","unstructured":"Stynes M, O\u2019Riordan E, Gracia JL (2017) Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. SIAM J Numer Anal 55(2):1057\u20131079","journal-title":"SIAM J Numer Anal"},{"issue":"6","key":"3792_CR50","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.3390\/sym15061263","volume":"15","author":"SM Syam","year":"2023","unstructured":"Syam SM, Siri Z, Altoum SH, Kasmani RM (2023) Analytical and numerical methods for solving second-order two-dimensional symmetric sequential fractional integro-differential equations. Symmetry 15(6):1263","journal-title":"Symmetry"},{"key":"3792_CR51","doi-asserted-by":"crossref","unstructured":"Tuan N, Nemati S, Ganji R, Jafari H (2020) Numerical solution of multi-variable order fractional integro-differential equations using the Bernstein polynomials. Eng Comput 1\u20139","DOI":"10.1007\/s00366-020-01142-4"},{"key":"3792_CR52","unstructured":"Verma P, Kumar M (2021) Existence and uniqueness results and analytical solution of the multi-dimensional Riesz space distributed-order advection-diffusion equation via two-step Adomian decomposition method. Eng Comput 1\u201316"},{"issue":"4","key":"3792_CR53","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.4208\/cicp.OA-2017-0019","volume":"22","author":"Y Yan","year":"2017","unstructured":"Yan Y, Sun Z-Z, Zhang J (2017) Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations: a second-order scheme. Commun Comput Phys 22(4):1028\u20131048","journal-title":"Commun Comput Phys"},{"issue":"1159","key":"3792_CR54","first-page":"561","volume":"224","author":"A Young","year":"1954","unstructured":"Young A (1954) The application of approximate product-integration to the numerical solution of integral equations. Proc R Soc Lond Ser A Math Phys Sci 224(1159):561\u2013573","journal-title":"Proc R Soc Lond Ser A Math Phys Sci"},{"issue":"1159","key":"3792_CR55","first-page":"552","volume":"224","author":"A Young","year":"1954","unstructured":"Young A (1954) Approximate product-integration. Proc R Soc Lond Ser A Math Phys Sci 224(1159):552\u2013561","journal-title":"Proc R Soc Lond Ser A Math Phys Sci"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03792-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-026-03792-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03792-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:03:57Z","timestamp":1778706237000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-026-03792-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,13]]},"references-count":55,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["3792"],"URL":"https:\/\/doi.org\/10.1007\/s40314-026-03792-4","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,13]]},"assertion":[{"value":"4 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest are declared by the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"398"}}