Some new Gronwall-Bellman-Bihari type integral inequality associatedwith ψ-Hilfer fractional derivative

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