Retarded Integral Inequality and its Application in Retarded Differential Equation

Differential equations are important tools in studying of natural science, engineering technology, and the laws of social economic development. It is necessary to seek some new inequalities in order to study of boundedness, uniqueness, stability and boundary value problem of a differential equation. Motivated by Abdeldaim integral inequalities, in this paper, we establish a class of generalized retarded nonlinear Gronwall-Bellman-Type integral inequalities and give upper bound estimation of the unknown function by analysis skills. Finally we give an example to illustrate the effectiveness of our results in estimation of solutions of some differential equations with the initial conditions.