%0 Journal Article %T Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach %A El-Sayed, A. M. A. %A Al-Issa, Sh. M. %J Journal of Nonlinear Sciences and Applications %D 2020 %V 13 %N 4 %@ ISSN 2008-1901 %F El-Sayed2020 %X In this article, we establish the existence of solutions for a functional integral equation of fractional order. The study upholds the case when the set-valued function has \(L^1\)-Caratheodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions. As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value, and the initial value problem for the arbitrary-order differential inclusion will be studied. %9 journal article %R 10.22436/jnsa.013.04.02 %U http://dx.doi.org/10.22436/jnsa.013.04.02 %P 180--186