Abstract
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.
Highlights
Fractional differential equations (FDEs) have been of great interest for the past three decades
Assume that βηα−1 ≠ 1 and y ∈ C(J, R); problem (7) has the unique solution given by the following formula: x (t) tα−1 − βηα−1 λ βtα−1 1 − βηα−1
Λ[x] = (Δ/(Δ − ρ))μλ[Fx], and x (t) = Tx (t) = tα−1 λ [x] + μFx (t) tα−1 Δ−ρ μλ. This shows that fixed points of S are solutions of (12)
Summary
Fractional differential equations (FDEs) have been of great interest for the past three decades. In [5], the author studied existence of positive solutions in case of the nonlinear fractional differential equation as follows: Dsu = λa (t) f (u) , 0 < t < 1, (1). Motivated by [5, 10], in this paper, we consider the existence of positive solution of the following boundary value problem for nonlinear fractional differential equation with changing sign nonlinearity and advanced arguments: Dαx (t) + μh (t) f (x (a (t))) = 0, t ∈ (0, 1) , 2 < α ≤ 3, μ > 0, x (0) = x (0) = 0,.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
