Some new retarded nonlinear integral inequalities and their applications in differential–integral equations

In this paper, we discuss some new retarded nonlinear Gronwall–Bellman–Pachpatte integral inequalities and give upper bound estimation of the unknown function by integral inequality technique. Our results generalize those of Abdeldaim and Yakout [A. Abdeldaim, M. Yakout, On some new integral inequalities of Gronwall–Bellman–Pachpatte type, Appl. Math. Comput. 217 (2011) 7887–7899] to some inequalities with both retarded argument and nonlinear integrand. An application to estimate the solutions of differential–integral equations is also given.