We introduce the notion of (α, Æ, β) - weak generalized Geraghty contractions in complete partially ordered partial b - metric spaces via triangular α-admissible mappings. We obtain sufficient conditions for the existence of fixed points of such maps in complete partially ordered partial b - metric spaces with coefficient s ≥ 1, where Æis an altering distance function and β ∈ Ω where Ω = {β : (0,∞) → [0, 1) satisfying β(tn) → 1 ⇒ tn → 0}. Examples are provided to illustrate our results.