Nonlinear contractions and Caputo tempered impulsive implicit fractional differential equations in b-metric spaces

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 nonlocal conditions and instantaneous impulses. The results are based on the o - d-Geraghty type contraction, the F-contraction and the fixed point theory. Furthermore, some illustrations are presented to demonstrate the plausibility of our results.

Keywords

• fixed point
• implicit differential equations
• impulses
• tempered fractional derivative
• o - d-geraghty contraction
• f-contraction
• nonlocal condition