On The Existence Of Positive Solutions Of Boundary Value Problems (for Systems) Of Fractional Differential Equations

Fractional differential equation is an important branch of ordinary differential equations. In recent years, fractional differential equation has been continue to in-depth study because of its theoretical system of continuous improvement and the close contact with many practical applications (such as:physics, mechanics, chemistry and engineering, etc.), by the international mathematical community and the importance of natural science. Fractional differential equations has become an important modern mathematics research direction.Fractional differential equations is a hot topic in recent years, research in this area is a very important area. In this paper, using the cone theory, fixed point theorem for nonlinear functional methods such as the nonlinear fractional differential equation(for Systems) integral existence of positive solutions for boundary value problems, and obtained some new results. The thesis is divided into four sections according to contents.Chapter 1 Preference, we introduce the main contents, then give the related concepts and important lemma of this paper.Chapter 2 We consider the following fractional differential equations with integral boundary where 0<α≤2, the nonlinear items f:(0,1)×[0,+∞)→[0,+∞), and can be singular at t=0,1. By cone theory of knowledge structure, related by a mixed monotone operator theory, the existence of positive solutions. Chapter 3 nonlinear fractional differential Sturm - Liouville integral boundary Where cDαis the Caputo fractional derivative of order 1<α≤2,f:[0,1]×R→R is continuous, g0, g1:[0,1]→[0,∞) are continuous and positive, a and b are nonnegative real parameter. Use Krasnoskii's fixed point theorem, under different conditions to discuss the existence of solutions of equations, this chapter gives the existence and multiplicity of (3.1.1).Chapter 4 At the basis of the former two chapters, in this section we consider the Fractional Differential Equations with Integral Boundary Where cDαis the Caputo fractional derivative of order 1