Existence and Hyers–Ulam stability for three-point boundary value problems with Riemann–Liouville fractional derivatives and integrals

This paper is concerned with a class of two-term fractional differential equations. Three-point boundary value problems with mixed Riemann–Liouville fractional differential and integral boundary conditions are discussed. The Green’s function is investigated and the existence results are obtained based on some fixed point theorems. The Hyers–Ulam stability is also studied for null boundary conditions. As an auxiliary result, a Gronwall type inequality of fractional order integral is obtained.