Existence of the mild solution for some fractional differential equations with nonlocal conditions
We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential equation with nonlocal conditions: Dqx(t)=Ax(t)+tnf(t,x(t),Bx(t)), t∈[0,T], n∈ℤ+, x(0)+g(x)=x0, where 0<q<1, A is the infinitesimal generator of a C0-semigroup of bounded linear operators on a Banach space X.
KeywordsCauchy problem Fractional abstract differential equation Nonlocal conditions Semigroup of bounded operators
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