Types Of Fractional Nonlinear Boundary Value Problems,

Along with science's and technology's development, various non-linear prob-lem has aroused people's widespread interest day by day, because it can well explain various the natural phenomenon. So, the mathemaatical world and the natural science world attach importance to the nonlinear functional analysis. They have obtained some new results for the nonlinear functional analysis and its applications. The fractional order nonlinear differential equation boundary value problem is also the hot spot which has been discussed in recent years. In this paper, we use the cone theory, the fixed point theory, as well as cone expan-sion and compression theorem, to study several kinds of boundary value problems for nonlinear fractional order integral differential equation and we apply the main results to the boundary value problem for the fractional order nonlinear integral differential equation. The thesis is divided into three chapters according to contents. In chapter 1, It is concerned with the a-order(1<α≤2) m-point BVP We can obtain the existence and uniqueness of solution, the discussion is based on the Banach contraction mapping principle. Current research fractional order differential equation multi-point boundary value problem of literature does not see more, our results also generalize many recent studies. In Chapter 2, we consider the following nonlinearα-order(3<α≤4) singu-lar boundry problem By using the Fixed point theorem of cone expansion and compression, the ex-istence of postive solutions are obtained. Compared with [26], this artical for discussion of analytical study contains the fractional derivative term provides ideas. In Chapter 3, the following postive solutions of a-order(3<α≤4) singular boundary value problem can obtained. By using the Fixed point theorem of cone expansion and compression, the ex-istence of postive solutions are obtained. And compared with [29], f singular at t=0, which also improved some known results.