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Existence of the mild solution for some fractional differential equations with nonlocal conditions. (English) Zbl 1180.34006

Summary: We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential equation with nonlocal conditions:

D q x(t)=Ax(t)+t n f(t,x(t),Bx(t)),t[0,T],n + ,x(0)+g(x)=x 0 ,

where 0<q<1, A is the infinitesimal generator of a C 0 -semigroup of bounded linear operators on a Banach space X.

34A08Fractional differential equations
34G20Nonlinear ODE in abstract spaces
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