(ω, c)−periodic solution for an impulsive system of differential equations with the quadrate of Gerasimov–Caputo fractional operator and maxima

Abstract

Existence and uniqueness of (ω, c)−periodic solution of boundary value problem for a nonlinear system of ordinary differential equations with the quadrate of Gerasimov–Caputo operator, impulsive effects and maxima are studied. Problem is reduced to solvability of the complex system of nonlinear functional integral equations. The method of contracted mapping is used in the proof of one-valued solvability of nonlinear functional integral equations. Some estimates are obtained for the (ω, c)−periodic solution of the proble