Functional fractional boundary value problems with singular ϕ-Laplacian

This paper discusses the existence of solutions of the fractional differential equations D(φ(Du)) = Fu, D(φ(Du)) = f(t, u, Du) satisfying the boundary conditions u(0) = A(u), u(T ) = B(u). Here μ, α ∈ (0, 1], ν ∈ (0, α], D is the Caputo fractional derivative, φ ∈ C(−a, a) (a > 0), F is a continuous operator, A,B are bounded and continuous functionals and f ∈ C([0, T ] × R). The existence results are proved by the Leray-Schauder degree theory.