Existence results for m-point boundary value problems of nonlinear fractional differential equations with p-Laplacian operator

In this paper, we discuss the existence and multiplicity of positive solutions to m-point boundary value problems of nonlinear fractional differential equations with p-Laplacian operator {D(0+)(beta(phi rho()D(0+)(alpha)u(t)) + phi(rho)(lambda)f(t,u(t)) = 0, 0 < t < 1, u(0) = 0, D-0+(y) u(1) = Sigma(m-2)(j=1) xi D-0+(gamma) u(eta), D-0+(alpha) u(0) = 0, where D-0+1(alpha) D-0+(beta) and D-0+(y) the standard Riemann-Liouville fractional derivatives with 1 < alpha <= 2, 0 < beta, gamma <= 1, 0 <= alpha - beta -1, lambda is an element of (0, + infinity), 0 < xi, eta, < 1, i = 1,2, ..., m - 2, Sigma(m-2)(i=1) xi(i)eta(alpha-beta-1)(i) < 1, 0 <= alpha - gamma -1, f is an element of C([0, 1] x [0, + infinity), [0 + infinity)), and phi(rho) (s) = vertical bar s vertical bar = vertical bar s vertical bar(-2) p > 1, phi(-1)(p) = phi(q), 1/p + 1/p = 1 Our results are based on the monotone iterative technique and the theory of the fixed point index in a cone. Furthermore, two examples are also given to illustrate the results.