Existence and uniqueness of solutions for a class of higher-order fractional boundary value problems with the nonlinear term satisfying some inequalities

Abstract

Abstract This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

Keywords

• Fractional boundary value problems
• Riemann–Stieltjes integral
• Nonlocal multipoint boundary conditions
• Existence and uniqueness of solutions