On the nonlinear Ψ-Hilfer hybrid fractional differential equations

In this paper, we initially derive the equivalent fractional integral equation to Psi-Hilfer hybrid fractional differential equations and through it, we prove the existence of a solution in the weighted space. The paper's primary objective is to obtain estimates on Psi-Hilfer fractional derivative and utilize it to derive the hybrid fractional differential inequalities involving Psi Hilfer fractional derivative. With the assistance of these fractional differential inequalities, we determine the existence of extremal solutions and comparison theorems.