Some new nonlinear impulsive differential and integral inequalities with nonlocal integral jump conditions are presented in this paper. Using the method of mathematical induction, we obtain a new upper bound estimation of certain differential and integral inequalities; these inequalities have both nonlocal integral jump and weakly singular kernels. Finally, we give two examples of these inequalities in estimating solutions of certain equations with Riemann-Liouville fractional integral conditions.
Keywords: Differential and integral inequalities; Nonlinear impulsive; Nonlocal intergal jump conditions; Riemann–Liouville fractional derivative.