Mathematical modeling

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

K. V. Boyko

Chelyabinsk State University

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.

Keywords: fractional differential equation, Gerasimov–Caputo derivative, quasilinear equation

UDC: 517.9

DOI: 10.25587/2411-9326-2025-1-98-99