Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann-Liouville Type Involving Semipositone Nonlinearities

In this work by the index of fixed point and matrix theory, we discuss the positive solutions for the system of Riemann-Liouville type fractional boundary value problems D(0+)(alpha)u(t)+f(1)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), D(0+)(alpha)v(t)+f(2)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), D(0+)(alpha)w(t)+f(3)(t,u(t),v(t),w(t)) = 0,t is an element of(0,1), u(0) = u'(0) = center dot center dot center dot = u((n-2))(0) = 0, D(0+)(p)u(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)u(t)dt, v(0)=v '(0) = center dot center dot center dot = v((n-2))(0) = 0, D(0+)(p)v(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)v(t)dt, w(0) = w'(0) = center dot center dot center dot = w((n-2))(0)=0, D(0+)(p)w(t)vertical bar(t=1) = integral(1)(0)h(t)D(0+)(q)w(t)dt, where alpha is an element of(n-1,n] with n is an element of N, n >= 3, p,q is an element of R with p is an element of[1, n-2], q is an element of[0, p], D-0+(alpha) is the alpha order Riemann-Liouville type fractional derivative, and f(i)(i=1,2,3) is an element of C([0,1] x R+ x R+x R+, R) are semipositone nonlinearities.