一类抽象非线性分数阶微分方程的Cauchy问题

Cauchy Problem for Some Abstract Nonlinear Fractional Differential Equations

该文研究如下抽象非线性微分方程_0~CD_t~αu(t)=A(t,u)u(t)+f(t,u(t),Bu(t)),0<α<1,0<t<T的局部和非局部Cauchy问题·运用不动点理论,分别给出了方程经典解和适度解存在的条件,并证明了解对初值的连续依赖性.

In this paper, we study the local and nonlocal Cauchy problem for the following abstract nonlinear fractional differential equation C0Ct^αu（t）=A（t,u）u（t）＋f（t,u（t）,Bu（t））,0〈α〈1,0〈t〈T By fixed point theory, the conditions for the existence of the classical solution and the mild solution of the equation are presented respectively. In addition, continuous dependence on initial values of the solution are proved.