Abstract
The fundamental purpose of this research is to investigate the existence theory as well as the uniqueness of solutions to a coupled system of fractional order differential equations with Caputo derivatives. In this regard, we utilize the definition and properties of a newly developed conception of complex valued fuzzy rectangular b-metric spaces to explore the fuzzy form of some significant fixed point and coupled fixed point results. We further present certain examples and a core lemma in the case of complex valued fuzzy rectangular b-metric spaces.