Document Type : Research Paper
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
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
0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,
u(0) = 0, u(1) =
0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) with
δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞) 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.