| Abstract: | We use the fixed point index theory of condensing mapping in cones discuss the existence of positive solutions for the following boundary value problem of fractional differential equations in a Banach space E $$begin{aligned} left{ begin{array}{ll} -D^{,beta }_{0^{+}}u(t)=f(t,u(t)),quad tin J, u(0)=u^{prime }(0)=theta ,quad u(1)=rho int _{0}^{1}u(t)dt, end{array} right. end{aligned}$$ where both (2 and (0 are real numbers, (J=[0,1]), (D^{,beta }_{0^{+}}) is the Riemann–Liouville fractional derivative, (f : Jtimes K rightarrow K) is continuous, K is a normal cone in Banach space E, (theta ) is the zero element of E. Under more general conditions of growth and noncompactness measure about nonlinearity f, we obtain the existence of positive solutions. |
