The Solution Of The Fractional Semilinear Abstract Cauchy Problem

The booming development of fractional calculus has caused widespread concern in the world in recent years,and has penetrated from pure mathematics to many fields of science and engineering.Fractional differential equations play an important role in describing some abnormal natural phenomenon.In this paper,we mainly consider the relevant conclusions of the solution of the fractional semilinear Abstract Cauchy problem(FCP).On the basis of the solution of the nonhomogeneous Cauchy problem,we get the whole existence of the problem(FCP)and the result of the local existence according to the discussion of the solution of the first order abstract Cauchy's problem.Although the deduction is more complicated,we can also get the corresponding mild solution,the local mild solution and the strong solution.Then,under the condition that A generates tight semigroups,the existence conclusion of the solution is obtained.