Some Generalizations of Novel (Δ backward difference )Δ-Gronwall-Pachpatte Dynamic Inequalities on Time Scales with Applications

Abstract

We established several novel inequalities of Gronwall-Pachpatte type on time scales. Our results can be used as handy tools to study the qualitative and quantitative properties of the solutions of the initial boundary value problem for a partial delay dynamic equation. The Leibniz integral rule on time scales has been used in the technique of our proof. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.