OICC Press Mathematical Analysis and its Contemporary Applications 6 2 2024 03 20 Existence and stability results for discrete fractional three-point boundary value problems 10.30495/maca.2024.2029404.1100 EN Buse Eralp Işıksungur Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey Fatma Serap Topal Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey Journal Article 2024 03 20 In this study, firstly we obtain the existing results for the following three-point boundary value problem -∇µ+1y(t) = Ay(t) + f(t, y(t)), t ∈ Nba+2, y(a + 1) = 0, y(b) = δ∇y(ν), 0 < µ < 1, A : C(Nba+2, R) → R, f : Nba+2 × R → R, by using the Brouwer fixed point theorem and the Banach fixed point theorem. Furthermore, we have established the stability of this problem in the sense of Hyers and Ulam. Examples are given which illustrate the effectiveness of the theoretical results.