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A Cauchy problem for evolution equations of fractional order. (English. Russian original) Zbl 0696.34047

Differ. Equations 25, No. 8, 967-974 (1989); translation from Differ. Uravn. 25, No. 8, 1359-1368 (1989).
There are proved existence and uniqueness results for the Cauchy problem \[ (D^{(\alpha)}x)(t)=Ax(t),\quad 0<t\leq T;\quad x(0)=x_ 0, \] where X is a Banach space, A is a closed linear operator in X with domain D(A), \(x_ 0\in X\) and \(\alpha\) a fractional number.
Reviewer: Gh.Aniculăesei

MSC:

34G20 Nonlinear differential equations in abstract spaces
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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