Nonlinear contractions and Caputo tempered implicit fractional differential equations in b-Metric spaces with infinite delay

Abstract

This paper deals with some existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in b-Metric spaces with initial condition and infinite delay. The results are based on the ???-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermore, an two illustrations are presented to demonstrate the plausibility of our results.