Eigenvalue of Fractional Differential Equations with p-Laplacian Operator

We investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -D-t(beta)(phi(p)(D(t)(alpha)x))(t) = lambda f(t,x(t)), t epsilon (0, 1), x(0) = 0, D(t)(alpha)x(0) = 0, D(t)(gamma)x(1) = Sigma(m-2)(j=1) a(j)D(t)(gamma)x(xi(j)), where D-t(beta), D-t(alpha), D-t(gamma) are the standard Riemann-Liouville derivatives and p-Laplacian operator is defined as phi(p)(s) = vertical bar s vertical bar(p-2)s, P > 1. f : (0, 1) x (0, +infinity) (sic) > [0, +infinity ) is continuous and f can be singular at t = 0,1 and x = 0. By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.