| 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 new upper bound estimation of certain differential and integral inequalities,these inequalities have both nonlocal integral jump and weakly singular kernels.Finally,we give some examples of these inequalities in estimating solutions of certain equations with Riemann-Liouville fractional integral conditions.The full text is divided into three chapters.The first chapter is introduction,which is divided into two sections.One section briefly introduces the research back-ground,development status and significance of the research,and the other section states the main work of this article.The second chapter is composed of three parts.The first part is the introduction,which mainly introduces the research process of the scholars at homeland and abroad as well as my own improvement.The second part is the preparatory knowledge,preliminary,giving a brief description of the important lemmas needed.The third part is the main result,which researches an proves some new nonlinear impulsive differential and integral inequalities with nonlocal integral jump conditions.The last chapter is the applications of the impulsive fractional order integral conditions,with some examples of nonlinear impulsive differential and integral inequalities for Riemann-Liouville fractional integral jump conditions explored. |
