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(δ)(t)= f(t,u(f)),t ∈ J,u(a)=u0,where J =[a,b],a>0,U0∈ R,δ∈(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 caDαy(t)+λcDα-2y(t)=f(t,y(t)),t∈J,y(a)=y’(a)=y"(a)=y"’(a)=0 where J =[a,b],a>0,3<α≤ 4,λ<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 Dαu(t)= f(t,u(t)),t G J,t2-αu(t)|t = 0,t2-αu(t)|t=1 = B,where J =[0,1],1<α<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.