Existence and Uniqueness of Positive Solutions for a Fractional Switched System

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: ((c)D(0+)(a)u(t)+f(o(t))(t,u(t))+g(sigma(t))(t,u(t)) =0,t epsilon J =[0,1]; (u (0) =u ''(0)=0,u(1)=f(0)(1)u(s) ds), where D-c(0+)a is the Caputo fractional derivative with 2 < alpha <= 3, sigma(t) : J -> {1, 2,...,N} is a piecewise constant function depending on t, and R+ = [0,+infinity), f(v) g(1) epsilon C[J x R+, R+], i = 1, 2,...,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results.