Abstract:
The existence of a unique local solution of the incomplete Cauchy type problem is proved
for a quasilinear equation with several fractional Riemann — Liouville derivatives and with a sectorial tuple of operators at lower derivatives
in the linear part in the case of the local Lipschitz continuity of a nonlinear operator with respect to the sum of the norms of graphs of unbounded operators from the equation. In this
case, the nonlinear operator depends on the fractional Riemann—Liouville derivatives
of lower orders with arbitrary fractional parts. The obtained abstract result is used in the study of an initial boundary value problem for an equation with
several fractional derivatives in time.
Keywords:Riemann — Liouville derivative, multi-term fractional differential equation, defect of Cauchy type problem, quasilinear equation.
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