Generalizations of Gronwall's type integral inequalities with singular kernel

Abstract

In this paper, the generalization of Gronwall's type integral inequalities with singular kernel are established. In applications, theorems on stability estimates for the solution of the nonlinear integral equation and the integral-differential equation of the parabolic type are presented. Moreover, these inequalities can be used in the theory of fractional differential equations. © 2018 Elsevier B.V., All rights reserved.