Stability and dependency of the solution of a nonlinear quadratic functional integral inclusion with distributed delay

Let E be a reflexive Banach space.In this paper, we are interested in the solvability of the nonlinear quadratic functional integral inclusion with distributed delayon the real half-axis.Our thought is found within the space BC(R + , E) of bounded continuous functions on the real half-axis R + and taking values in a reflexive Banach space E beneath the presumption that the multi-valued function F fulfill Lipschitz condition in E. The main tool applied in this work is the procedure associated with measures of non-compactness in the space BC(R + , E) by a given norm of continuity and using Darbo's fixed point theorem.The asymptotic stability and the asymptotic dependency of the solution will be studied.We additionally provide an example to demonstrate the effectiveness and value of our results.