Some Results on Fractional m-Point Boundary Value Problems

Abstract

In this paper, we will apply some fixed-point theorems to discuss the existence of solutions for fractional m-point boundary value problems $D_{0^{+}}^q\left(u^{″}\left(t\right)\right)=h\left(t\right)f\left(u\left(t\right)\right),t\in \left[0,1\right],1<q\le 2,u^{\prime }\left(0\right)=u^{″}\left(0\right)=u\left(1\right)=0,u^{″}\left(1\right)-{\sum }_{i=1}^{m-2}{\alpha }_i{u}^{‴}\left({\xi }_i\right)=0.$ In addition, we also present Lyapunov’s inequality and Ulam-Hyers stability results for the given m-point boundary value problems.