In this paper we will consider an ath order fractional boundary value problem, n−1 < a ≤ n, n ∈ N, with boundary conditions that include a fractional derivative at 1. We will develop properties of the Green’s Function for this boundary value problem and use these properties along with the Contraction Mapping Principle, and the Schuader’s, Krasnosel’skii’s, and Leggett-Williams fixed point theorems to prove the existence of positive solutions under different conditions.
Digital Object Identifier (DOI)
A. Hollon, Christina and T. Neugebauer, Jeffrey
"Existence of Positive Solutions to a Family of Fractional Two Point Boundary Value Problems,"
Progress in Fractional Differentiation & Applications: Vol. 2
, Article 4.
Available at: https://dc.naturalspublishing.com/pfda/vol2/iss3/4