On existence and uniqueness of a global solution to a quasilinear equation with Gerasimov–Caputo fractional derivatives

Abstract

Issues of the unique global solvability of the Cauchy problem for a class of quasilinear equations in Banach spaces are studied. The equations contain several fractional derivatives of Gerasimov – Caputo in the linear and nonlinear part. The sectoriality condition for a pencil of operators at derivatives in the linear part is used.