On the nonlinear Ψ-Hilfer hybrid fractional differential equations

In this paper, we initially derive the equivalent fractional integral equation to Ψ -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 Ψ -Hilfer fractional derivative and utilize it to derive the hybrid fractional differential inequalities involving Ψ -Hilfer fractional derivative. With the assistance of these fractional differential inequalities, we determine the existence of extremal solutions and comparison theorems.