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

Keywords:

Cauchy problem; Banach space