چکیده (انگلیسی):

In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of 4 Gronwall–Bellman–Bihari type with delay for discontinuous functions are established. These inequalities 5 generalize and improve some former famous results about inequalities, and which provide an excellent tool 6 to discuss the qualitative and quantitative properties for solutions to some nonlinear differential and integral 7 equations. To illustrate our results, we present an example to show estimated solutions for an impulsive 8 differential system.