Positive Solution of Boundary Value Problem Involving Fractional Pantograph Differential Equation

In this paper, we study and integrate the positive solution of fractional pantograph differential equation with mixed conditions of the from: D-RL(0+)q u(t) + f(t, u(t), u(lambda t)) = 0, t is an element of (0,1), 0 < lambda < 1, u(0) = 0 D-RL(0+)p u(1) = Sigma(n)(i=1) alpha(i)u(eta(i)), 0 < p <= 1, eta(i) is an element of (0, 1), where 1 < q < 2, alpha(i) is an element of R, n is an element of N, and D-RL(0+)q, D-RL(0+)p are the Riemann-Liouville fractional derivative of order q, p, f : [0, 1] x R x R -> R is a continuous function. By using the fixed point theorems, the main tools for finding positive solutions and uniqueness of this problem are obtained. We give one example of the main results.