Natural phenomena as well as problems encountered in pure
and applied sciences are modeled by ordinary, partial or integral
differential equations. Most of these problems have a nonlinear
aspect which makes their studies difficult, or even impossible.
For this, they must resort to other alternatives; among the methods used
is the integral inequalities approach, which allows the study of
quantitative and qualitative properties of solutions such as
existence, uniqueness, delimitation, oscillation, and stability.
In this study, we present some new integral inequalities of the
Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results
are derived and some applications to ordinary differential equations
are provided to demonstrate the effectiveness of our finding.