Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments D(alpha)x(t) + mu h(t)f(x(a(t))) = 0, t is an element of (0, 1), 2 < alpha <= 3, mu > 0, x(0) = x'(0) = 0, x(1) = beta x(eta) + lambda[x], beta > 0, and eta is an element of (0, 1), where D-alpha is the standard Riemann-Liouville derivative, f : [0,infinity) -> [0,infinity) is continuous, f (0) > 0, h : [0, 1] -> (-infinity + infinity), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.