RETARDED NONLINEAR INTEGRAL INEQUALITIES OF GRONWALL-BELLMAN-PACHPATTE TYPE AND THEIR APPLICATIONS

In this article, we state and prove several new retarded non-linear integral and integrodifferential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous in-equalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Appli-cations are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.