Zheng Zhaowen, Zhang Yingjie, Shao Jing
1School of Mathematical Sciences, Qufu Normal University, Qufu, P.R. China.
2Department of Mathematics, Jining University, Qufu, P.R. China.
J Inequal Appl. 2018;2018(1):170. doi: 10.1186/s13660-018-1762-3. Epub 2018 Jul 13.
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.
本文给出了一些具有非局部积分跳跃条件的新型非线性脉冲微分与积分不等式。利用数学归纳法，我们得到了某些微分与积分不等式的一个新的上界估计；这些不等式既具有非局部积分跳跃又具有弱奇异核。最后，我们给出了这些不等式在估计具有黎曼 - 刘维尔分数积分条件的某些方程解时的两个例子。
