Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to aclass of nonlinear fractional order multipoint boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 q ≤ 2, 0 t 1,u(0) = 0, u(1) =∑m−2 i=1δiu(ηi),where Dq0+ represents standard RiemannLiouville fractional derivative, δi, ηi ∈ (0, 1) with∑ ^m−2i=1δiηi q−1 1, and f : [0, 1] × [0, ∞) → [0, ∞) is a continuous function. We use some classicalresults of fixed point theory to obtain sufficient conditions for the existence and multiplicity results of positive solutions to the problem under consideration. In order to show the applicabilityof our results, we provide some examples.