Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210201A generalization of Darbo's theorem with application to the solvability of systems of integral-differential equations in Sobolev spaces287300478410.22075/ijnaa.2021.4784ENHojjatollahAmiri KayvanlooDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, IranMahnazKhanehgirDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, IranRezaAllahyariDepartment of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.Journal Article20180720In this article, we introduce the notion of $(alpha,beta)$-generalized Meir-Keeler condensing operator in a Banach space, a characterization using strictly L-functions and provide an extension of Darbo's fixed point theorem associated with measures of noncompactness. Then, we establish some results on the existence of coupled fixed points for a class of condensing operators in Banach spaces. As an application, we study the problem of existence of entire solutions for a general system of nonlinear integral-differential equations in a Sobolev space. Further, an example is presented to verify the effectiveness and applicability of our main results.https://ijnaa.semnan.ac.ir/article_4784_690b0b82e08a2f61e248755fad00d3bc.pdf