Further Nonlinear Retarded Integral Inequalities for Gronwall–Bellman Type and Their Applications

Abstract

In this article, we will derive several new nonlinear retarded integral inequalities for Gronwall–Bellman type and then apply them as handy tools to examine explicit bounds for solutions of initial value problems, and will also use to evaluate the qualitative as well as the quantitative behavior of solutions of nonlinear retarded differential and integral equations. These inequalities extend some present inequalities to the current literature. An application is also given to demonstrate the strength of our results.