(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications

Abstract

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations. © 2022 by the authors.