In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution of this equation real kernel α−harmonic mappings. In this paper, we study some geometric properties of this real kernel α−harmonic mappings. We give univalence criteria and sufficient coefficient conditions for real kernel α−harmonic mappings that are fully starlike or fully convex of order γ, γ ∈ [0, 1). Furthermore, we establish a Landau type theorem for real kernel α−harmonic mappings