We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced argumentsDαx(t)+μh(t)f(x(a(t)))=0,t∈(0,1),2<α≤3,μ>0,x(0)=x′(0)=0,x(1)=βx(η)+λ[x],β>0, and η∈(0,1),whereDαis the standard Riemann-Liouville derivative,f:[0,∞)→[0,∞)is continuous,f(0)>0, h :[0,1]→(−∞,+∞), anda(t)is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.
Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line
