Research On Some Weakly Singular Integral Inequalities

It is well known that Gronwall type integral inequalities play a dominant role in the theoretical study of differential and integral equations.Some new weakly singular inequalities of gronwall-Bellman type are established, which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of integral equations and evolution equations, it also can be used for fractional differential and integral equations.This paper on the basis of references [17, 18] spreads the relevant integral inequality extended to fractional integral inequality, and get some new results.The thesis is divided into three chapters according to the contents.Chapter 1 Preference, we introduce the main contents and its background of this paper.Chapter 2 Based on some known weakly singular integral inequalities in [17], this chapter gives the existence of certain new weakly singular inequalities we can get two rusults:If [α, β, γ] ∈ I, then If [α, β, γ] ∈ II, thenThen we apply those inequalities to the research on the boundedness for solutions to fractional differential equations.Chapter 3 Based on some known nonlinear integral inequalities of Wendroff type with continuous and weakly singular kernel in [18], this chapter gives the existence of certain new integral inequalitiesThen we offered explicit bounds for the unknown functions.