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Well-posedness of the Basset problem in spaces of smooth functions. (English) Zbl 1217.34006

Summary: We consider the initial value problem for the fractional differential equation

du(t) dt+D t 1 2 u(t)+Au(t)=f(t),0<t<1,u(0)=0

in a Banach space E with the strongly positive operator A. The well-posedness of this problem in spaces of smooth functions is established. In practice, the coercive stability estimates for the solution of problems for 2m-th order multidimensional fractional parabolic equations and one-dimensional fractional parabolic equations with nonlocal boundary conditions in the space variable are obtained.

MSC:
34A08Fractional differential equations
34G10Linear ODE in abstract spaces
35K90Abstract parabolic equations
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