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As we know, it has been published many papers about the existence of solution for different fractional differential equations (see for example, [8–16] and the references there in). Also, it has been appeared many works on fractional differential inclusions (see for example, [1–7, 18–23, 26, 29, 31–33, 36] and the references there in). One can find more details about necessary notions in [25, 30, 34]. Let η, ν, β ∈ (0, 1) and α ∈ (1, 2] be such that Γ(2 − β)(ην − νη − η + ν + 4η − 2ν − 2) + 2(1 − η) 6= 0 and α− β > 1. In this paper, we investigate the existence of solutions for the Caputo fractional differential inclusion

On a Caputo fractional differential inclusion with integral boundary condition for convex-compact and nonconvex-compact valued multifunctions