Let f : [0,1]×R2 → R be a function satisfying Carathéodory’s conditions and e(t) ∈ L1[0,1]. Let ξi ∈ (0,1), ai ∈ R, i = 1,2, . . . ,m− 2, 0 < ξ1 < ξ2 < · · · < ξm−2 < 1 be given. This paper is concerned with the problem of existence of a solution for the m-point boundary value problem x′′(t) = f (t,x(t),x′(t))+e(t), 0 < t < 1; x(0) = 0, x′(1) =∑m−2 i=1 aix′(ξi). This paper gives conditions for ...

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.