Existence of Solutions for Two Point Boundary Value Problems for Fractional Differential Equations with P-laplacian

In this paper, we study the existence of positive solutions to boundary value problem for fractional differential equation  cDσ 0+(φp(u ′′(t)))− g(t)f(u(t)) = 0, t ∈ (0, 1), φp(u ′′(1)) = 0, φp(u ′′(0)) = 0, αu(0)− βu′(0) = 0, γu(1) + δu′(1) = 0, where cDα 0+ is the Caputo’s fractional derivative of order 1 < σ ≤ 2, φp(s) = |s| p−2s, p > 1, α, β, γ, δ ≥ 0 and f ∈ C([0,∞); [0,∞)), g ∈ C((0, 1); (0,∞)). 2000 Mathematics Subject Classification: 47H10, 26A33, 34A08.