Existence of solutions for a fractional boundary value problem via the Mountain Pass method and an iterative technique

In this paper, we consider the existence of solution to the following fractional boundary value problem {ddx(p0Dx−β(u′(x))+qxD1−β(u′(x)))+f(x,u(x))=0,x∈(0,1),u(0)=u(1)=0, where the constants β∈(0,1)β∈(0,1), 0Dx−β and xD1−β denote left and right Riemann–Liouville fractional integrals of order ββ respectively, 0