The goal of this paper is to investigate existence of solutions for the multi-term nonlinear fractional q-integro-differential ${}^cD_q^{\alpha} u(t)$ in two modes equations and inclusions of order $\alpha \in (n -1, n]$, with non-separated boundary and initial boundary conditions where natural number $n$ is more than or equal to five. We consider Carath\'{e}odory multivalued map and using some fixed point theorems such as Leary-Schauder and Covitz-Nadler famous theorems for finding solutions of the inclusion problems. besides, we present results whenever the multi-functions are convex and non-convex. Lastly, we give some examples illustrating the primary effects.
