Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems. (9th September 2013) - Darzi, R.; Mohammadzadeh, B.; Neamaty, A.; Bǎleanu, D.
Abstract : We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D 0 + α u t + f t, u t = 0, 0 < t < 1, 2 < α ≤ 3, u 0 = u ′ 0 = 0, D 0 + α − 1 u 1 = β u ξ, 0 < ξ < 1, where D 0 + α denotes Riemann-Liouville fractional derivative, β is positive real number, β ξ α − 1 ≥ 2 Γ α, and f is continuous on 0, 1 × 0, ∞ . As an application, one example is given to illustrate the main result.