Fractional du Bois-Reymond lemma of order α ∈ (n − 1 over 2, n)

In the paper, we derive a fractional du Bois-Reymond lemma for functions of one variable with Riemann-Liouville derivatives of order α ∈ (n - 1 over 2, n) where n ∈ ℕ, n ≥ 2 To prove this lemma we derive a theorem on the integral representation of a function possessing the fractional derivative of order α >; 0 and a theorem on the fractional integration by parts of high order.