A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

Abstract

We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.

Some New Discrete Gronwall-Bellman Type Inequalities with Three Independent Variables and Applications

“…Wang [10][11][12][13] established some nonlinear retarded difference inequalities and gave some applications of the obtained inequalities to the estimation of finite difference equations. Pachpatte [14][15][16] obtained certain inequalities arising in the theory of differential equations and provided new estimates for these types of inequalities.…”