Existence Of Positive Solutions For Nonlocal Boundary Value Problems Of Several Class Of Fractional Differential Equations

In recent years, fractional differential equations have been widely used in optics and thermal systems, electromagnetics, control engineering and robotic, etc. The research on fractional differential equations is very important in both theory and applications.By using nonlinear analysis tools, some scholars established the existence, uniqueness,multiplicity and qualitative properties of solutions for nonlinear fractional differential equations.In this paper, we mainly study the existence of positive solutions for two classes of fractional differential equations system with nonlocal boundary conditions. The paper is organized as follows:In Chapter 1, we study the system of fractional semipositone differential equations with parameter and integral boundary conditions where ?>0 is a parameter,2<?,??3,0<?,?<1,?-?>2,?-?>2,fi?C((0,1)×[0,+?)3,(-?,+?))are continuous and may be singular at t=0,1,i= 1,2. A,B are nondecreasing functions of bunded variations,(?) and (?) are Riemann-Stieltjes integrals,D0+?-?,D0+?, D0+?-? and D0+? are the standard R.iemann-Liouville derivatives. By Guo-Krasnosel'skii's fixed point theorem, we get the existence results of positive solutions for above problems.In Chapter 2, we investigate the system of fractional p-Laplacian nonlocal boundary value problems where ? and ? are positive parameters, ?i?(1,2] and ?i? (3,4] (i= 1,2). f,g?C([0,1] × [0,+?)2, [0,+?)), ?pi(s)=|s|pi-2s, pi>1,?pi-1=?qi,1/pi+1/qi=1,?i?(0,1),bi?(0,?i1-?i/pi-1).D0_?i and D0+?i are the standard Riemann-Liouville derivatives. Under different combinations of superlinearity and sublinearity of the functions f and g, various existence results for positive solutions are derived in terms of different values of ? and ?via Guo-Krasnosel'skii's fixed point theorem.