Abstract fractional Landau inequalities

Abstract. We present uniform and \(L_{p}\) mixed Caputo–Bochner abstract fractional Landau inequalities over \(\mathbb{R}\) of fractional orders \(2<\nu \leq 3\). These estimate the size of first and second derivatives of a Banach space valued function over \(\mathbb{R}\). We give applications when \(\nu =2.5\).