Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682210120191101Solvability of infinite system of nonlinear singular integral equations in the $C(I\times I, c)$ space and modified semi-analytic method to find a closed-form of solution6376405310.22075/ijnaa.2019.16525.1875ENAnupam DasDepartment of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, IndiaMohsen RabbaniDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran0000-0003-3602-6125Bipan HazarikaDepartment of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, IndiaDepartment of Mathematics, Gauhati University, Guwahati-781014, Assam, India0000-0002-0644-0600Reza ArabDepartment of Mathematics, Sari Branch, Islamic Azad University, Sari, IranJournal Article20181118In this article, we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I \times I, c)$ by applying measure of noncompactness and Meir-Keeler condensing operators. By presenting an example, we have illustrated our results. For validity of the results we introduce a modified semi-analytic method in the case of two variables to make an iteration algorithm to find a closed-form of solution for the above problem. The numerical results show that the produced sequence for approximating the solution of example is in the $c$ space with a high accuracy.https://ijnaa.semnan.ac.ir/article_4053_f0d83ce21ced64ebc87901f2504b2f55.pdf