Abstract
In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving phi-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage's hybrid fixed point theorem for three operators in a Banach algebra and Dhage's helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.