Note di Matematica ISSN 1123-2536, e-ISSN 1590-0932 Note Mat. 35 (2015) no. 1, 95–107. doi:10.1285/i15900932v35n1p95 Solvability for a coupled system of nonlinear fractional integro-differential equations Mohamed Amin Abdellaoui Department of Mathematics and Informatics, Faculty of Exact Sciences and Informatics, UMAB, University of Mostaganem, Algeria abdellaouiamine13@yahoo.fr Zoubir Dahmani Laboratory LPAM, UMAB, University Mostaganem, Algeria zzdahmani@yahoo.fr Received: 11.1.2014; accepted: 12.2.2015. Abstract. In this paper, we prove the existence of solutions for fractional coupled systems of integro-differential equations in Banach spaces. The results are obtained using fractional calculus and fixed point theorems. Some concrete examples are also presented to illustrate the possible application of the established analytical results. Keywords: Caputo derivative, fixed point theorem, coupled system, existence, uniqueness. MSC 2000 classification: primary 34A34, secondary 34B10. 1 Introduction The fractional differential equations theory is increasingly used for many mathematical models in science and engineering, such as physics, chemistry, control theory, signal processing and biophysics. For more details, we refer the reader to ([7, 9, 11]) and the references therein. Recently, there has been a significant progress in the investigation of these equations (see [2, 4, 5]). More- over, the study of coupled systems of fractional differential equations is also of great importance. Such systems occur in various problems of applied science. For some recent results on the fractional systems, we refer the reader to (see [1, 3, 6, 12]). In this paper, we study the following coupled system of fractional integro- http://siba-ese.unisalento.it/ c  2015 Universit`a del Salento