Mathematical modeling

Incomplect Cauchy type problem for quasilinear fractional equations

Zakharova Tatyana A, V. E. Fedorov

Chelyabinsk State University

Abstract: Using the theory of fractional powers of the sectorial operator, the existence of a unique solution to an incomplete Cauchy-type problem for a quasi-linear differential equation in Banach space resolved with respect to the highest Riemann–Liouville derivative is proved.

Keywords: quasilinear equation, Cauchy type problem, defect of Cauchy type problem, complex power of operator

UDC: 517.9

DOI: 10.25587/2411-9326-2025-1-113-114