New sharp estimates of the interval length of the uniqueness results for several two-point fractional boundary value problems

Abstract

This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works.

Keywords

• fractional differential equation
• two-point boundary condition
• uniqueness of solution