Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for a Mixed Fractional Boundary Value Problem

Abstract

In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.