Abstract
In this paper, we consider a Riemann–Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green’s function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions that the nonlinearity f(t,x) may change sign and may be singular at t = 0,1 and x=0, and we also obtain the uniqueness results of positive solution for a singular problem by means of the monotone iterative technique.
Highlights
1 Introduction In this paper, we study properties of the Green’s function of the following two-term fractional differential equation boundary value problem (FBVP):
We investigate the existence and multiplicity of positive solutions for a singular FBVP with changing sign nonlinearity, and we consider the uniqueness results of positive solution for a singular FBVP
The interesting point is that the linear operator of the FBVPs contains two terms
Summary
1 Introduction In this paper, we study properties of the Green’s function of the following two-term fractional differential equation boundary value problem (FBVP): In [19], we established some new positive properties of the corresponding Green’s function for (2) with multi-point boundary value condition. In [20], we established some new positive properties of the Green’s function for the Riemann–Liouville type FBVP, in which the linear operator contains two terms:
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