{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T06:59:34Z","timestamp":1762066774920,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomials are implemented to transform these equations into a system of linear algebraic equations. The error analysis of the proposed method is examined in detail. Numerical results highlight the robustness and accuracy of the proposed strategy.<\/jats:p>","DOI":"10.3390\/fractalfract6090511","type":"journal-article","created":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T22:53:46Z","timestamp":1663023226000},"page":"511","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0874-6870","authenticated-orcid":false,"given":"Davood Jabari","family":"Sabegh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bonab Branch, Islamic Azad University, Bonab 55517-85176, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3162-6212","authenticated-orcid":false,"given":"Reza","family":"Ezzati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj 31499-68111, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"Omid","family":"Nikan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"Institute of Mechanical Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8262-1369","authenticated-orcid":false,"given":"Alexandra M. S. F.","family":"Galhano","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias Naturais, Engenharias e Tecnologias, Universidade Lus\u00f3fona do Porto, Rua Augusto Rosa 24, 4000-098 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Milici, C., Dr\u0103g\u0103nescu, G., and Machado, J.T. (2018). Introduction to Fractional Differential Equations, Springer.","DOI":"10.1007\/978-3-030-00895-6"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Biswas, K., Bohannan, G., Caponetto, R., Lopes, A.M., and Machado, J.A.T. (2017). Fractional-Order Devices, Springer.","DOI":"10.1007\/978-3-319-54460-1"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sabatier, J., Agrawal, O.P., and Machado, J.T. (2007). 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