Abstract
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 D-0(broken vertical bar)q u(t) = f (t, u(t)), 1 < q <= 2, 0+ 0 < t < 1, u(0) = 0, u(1) = Sigma(m-2)(i=1) delta iu(eta i), where D-0+(q) represents standard Riemann-Liouville fractional derivative, delta(i,) eta(i) is an element of(0, 1) with Sigma(m-2)(i=1) delta(i,) eta(q)(i) < 1, and f : [0, 1] x [0, infinity) -> [0, infinity) 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.