Three-point boundary value problems for implicit Caputo tempered fractional differential equations in b-metric spaces

Abstract

This paper is concerned with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in $b$-Metric spaces with three-point boundary conditions. The results are based on the ${\omega}-{\varpi}$-Geraghty type contraction, the ${\digamma}$-contraction and the fixed point theory. In addition, two illustrations are provided to highlight the plausibility of our findings.