Study On Solvability Of Several Fractional Differential Equations

In this thesis.we discuss the solvability of several fractional differential equa-tions.The main works are:In chapter 1,by using monotone iterative method,we study the existence of solution of the initial value problem u(?)(t)= f(t,u(f)),t ? J,u(a)=u0,where J =[a,b],a>0,U0? R,??(0,1]are constants,f:J × R ?R is continuous.In chapter 2,by using upper and lower solution of monotone iterative method,we study the existence of solution of the initial value problem caD?y(t)+?cD?-2y(t)=f(t,y(t)),t?J,y(a)=y'(a)=y"(a)=y"'(a)=0 where J =[a,b],a>0,3<?? 4,?<0,f:J × R ?R is continuous function.In chapter 3,by using the shooting method,we study the existence of solution of the boundary value problem D?u(t)= f(t,u(t)),t G J,t2-?u(t)|t = 0,t2-?u(t)|t=1 = B,where J =[0,1],1<?<2,f:J × R? R is a continuous function and satisfies|f(t,u(t))-f(t,v(t))|?L/tr|u-v|,t?(0,1),where 0<L<1 is constant.