A New Result Regarding Positive Solutions for Semipositone Boundary Value Problems of Fractional Differential Equations

In this paper, we discuss the positive solutions to a class of semipositone boundary value problems of fractional differential equations. The nonlinearity f(t,x) may be singular at t=0,1 and satisfies f(t,x)≥−a(t)x−R(t). We derive some new properties of the Green’s function of the auxiliary problems, and discover the multiplicity and existence of the positive solutions by utilizing the fixed point index theory. Two examples are illustrated to validate the main results.