Recent Results on Nonlinear Retarded Integral Inequalities with Applications

This article establishes new retarded nonlinear integral inequalities that extend and generalize several known results in the literature, including recently reported estimates. These inequalities are used to derive explicit bounds for the unknown functions. These bounds are shown to be sharper and more general than existing ones, recovering earlier results as special cases. As an application, the derived inequalities are used to study the boundedness, uniqueness, and global existence of solutions to an initial value problem for a class of nonlinear integro-differential equations with delay. An illustrative example is presented to illustrate the applicability and effectiveness of the results.