Системы нелинейных дифференциальных уравнений дробного порядка в весовых пространствах непрерывных функций

Abstract

A system of nonlinear equations of fractional order containing the Riemann - Liouville fractional derivative, is considered on a finite interval of the real axis in a weighted space of continuous functions. The equivalence of the Cauchy-type problem for such a system and of a system of nonlinear Volterra integral equations is established, and the existence and uniqueness of its solution is proved. The corresponding assertions for a system of ordinary differential equations are presented.