Stability of difference schemes for fractional equations (Q745268)

The authors studies the stability of the approximate schemes for the Cauchy problem with the fractional derivative \[ (D^{\alpha}_{t} u)(t)= A u(t), \qquad u(0)= x, \qquad 0< \alpha \leq 1, \] in the Banach space. The approximate schemes are constructed using the explicit and implicit finite difference formulas. The proof of the stability is based on the known theorem of Trotter-Kato.