{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T11:47:36Z","timestamp":1770292056038,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T00:00:00Z","timestamp":1638057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The aim of this article is to present a procedure for the factorization and exact solution of boundary value problems for a class of n-th order linear Fredholm integro-differential equations with multipoint and integral boundary conditions. We use the theory of the extensions of linear operators in Banach spaces and establish conditions for the decomposition of the integro-differential operator into two lower-order integro-differential operators. We also create solvability criteria and derive the unique solution in closed form. Two example problems for an ordinary and a partial intergro-differential equation respectively are solved.<\/jats:p>","DOI":"10.3390\/a14120346","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T01:49:58Z","timestamp":1638150598000},"page":"346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Procedure for Factoring and Solving Nonlocal Boundary Value Problems for a Type of Linear Integro-Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Efthimios","family":"Providas","sequence":"first","affiliation":[{"name":"Department of Environmental Sciences, Gaiopolis Campus, University of Thessaly, 415 00 Larissa, Greece"}]},{"given":"Ioannis Nestorios","family":"Parasidis","sequence":"additional","affiliation":[{"name":"Department of Environmental Sciences, Gaiopolis Campus, University of Thessaly, 415 00 Larissa, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.apnum.2005.04.020","article-title":"Numerical solution of a Fredholm integro-differential equation modelling neural networks","volume":"56","author":"Jackiewicz","year":"2006","journal-title":"Appl. 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