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 a class of nonlinear fractional order multi-point boundary value problems of the type−Dq۰+u(t) = f(t, u(t)), ۱ < q ≤ ۲, ۰ < t < ۱,u(۰) = ۰, u(۱) =m−۲∑ i=۱δiu(ηi),where Dq۰+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (۰, ۱) withm−۲∑i=۱δiηi q−۱ < ۱, and f : [۰, ۱] × [۰, ∞) → [۰, ∞) is a continuous function. We use some classical results 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 applicability of our results, we provide some examples.

Keywords:

Fractional differential equations , Boundary value problems , Positive solutions , Green’s function , fixed point theorem