Existence Results For Some Classes Of Coupled Fractional Differential Systems With Nonlocal Boundary Value Conditions

Fractional calculus has gained considerable popularity and importance due to its wide applications in the fields of physics,chemistry,biology and electrodynamics,etc.Applying fixed point theorem and coincidence degree theory of Mawhin,this paper is concerned with existence results for some classes of coupled fractional differential systems with nonlocal boundary value conditions.In chapter 1,we mainly introduce the research status of fractional differential equations with boundary value conditions and some basic knowledge.In chapter 2,we consider the existence of solutions for the following systems where CD0+i(i = ?,?,?,?)is the CapUto fractional derivate,I0+?i(i = 1,2)is Riemann-Liouville fractional integral,1<?,?<2,0<?,?<1,0<1,0??,?? 1,?i>0(i =1,2),a,b ? R.f,g?C([0,1]× R×R ×R),h,?:C([[0,1],R)?R>are given con-tinuous functionals.Applying Schauder fixed point theorem and Leray-Schaudernonlinear alternative theory,some existence results of solutions to this systems are obtained.In chapter 3,we consider the existence of solutions for the following systems where D0+i(i ? ?,?,?-1,?-1)is the standard Riemann-Liouville fractional derivative,1<?,?<2,f,g:[0,1]× R2? R satisfy the Caratheodory conditions,Riemann-Stieltjes integrals are given by p[x]=?01x(t)dA(t),q[y]= ?01y(t)dB(t),A,B:[0,1]?R are functions of bounded variations.By using the coincidence degree theory of Mawhin,the existence results were studied.In chapter 4,we consider the existence of solutions for the following systems where n,m ?N,n,m? 3.The integrals are Riemann-Stieltjes integrals,H,K:[0,1]?R are functions of bounded variations with ? = 1-(?01 sdH(s))(?01 sdK(s))?0.The existence of positive solution is obtained by fixed point theorem on cone.