Ulam-Hyers Stability Of Two Classes Non-instantaneous Impulses Fractional Differential Systems

As a mathematical model,the fractional differential equation plays an increasingly important role in describing some complex systems and phenomena,especially in study of stability,controllability and properties of the system.The Ulam-Hyers stability concept ensured the existence of solution of the system,so it is effectively to solves the problem which is difficult to find an exact solutions for some nonlinear systems.Thus,the study on Ulam-Hyers stability of fractional differential equations has im-portant theoretical value and practical significance.This thesis mainly used contraction mapping principle and fixed point theorem to study the existence and Ulam-Hyers stability of solutions of two types of non-instantaneous impulsive fractional differential equations.The main research of the dissertation are as follows:1.A class of fractional-order multiple point boundary value problem involve non-instantaneous impulse and abstract bounded operator were studied(?)The Banach contraction principle was used to prove the existence and the Ulam-Hyers stability of this system.2.A class of fractional-order multiple point boundary value coupled system in-volve noninstantaneous impulse and abstract bounded operator were studied(?)The Banach contraction principle,Arzela-Ascoli theorem and Schauder fixed point theorem were used to prove the existence and the Ulam-Hyers stability of the cou-pled system.The obtained results of existence and Ulam-Hyers stability in this thesis were provided theoretical support for seeking the solution of fractional differential equation and studying of Ulam-Hyers stability.