Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

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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.