Existence And Uniqueness Of Solutions For Several Classes Of Fractional Order Differential Equation

In this thesis,we obtain the existence and uniqueness of solutions for the fractional impulsive differential equations under different boundary value conditions by using the methods of upper and lower solution method,monotoneiteration,Banach compression mapping principle and fixed point theorem in nonlinear functional analysis.The thesis mainly consists of five parts.In Chapter 1,We mainly introduce the research history and background of fractional calculus,expound the research status at home and abroad,and the main research content of this thesis.In Chapter 2,we study the existence and uniqueness of solutions for a class of Riemann-Liouville fractional differential equation boundary value problems with P(t)terms,give and prove the sufficient conditions for the existence and uniqueness of the solution of the boundary value problem,and finally give an example to verify the feasibility of the obtained conclusions.In Chapter 3,we study the existence and uniqueness of solutions to a class of Caputo fractional order impulsive differential equation three-point boundary value problems,give and prove sufficient conditions for the existence and uniqueness of the solutions of this equation,and give an example to verify that the conclusions obtained are feasible.In Chapter 4,we study the existence of extreme solutions for a class of fractional order impulsive functional differential equation with parameters ?,construct a new comparison result,then obtain the existence of the extreme solution of the equation by using the monotone iterative technique and the method of upper and lower solutions.In Chapter 5,All the research results of this thesis are summarized,and we give future work ideas for the content to be further studied.