Existence And Multiplicity Of Solutions For Two Classes Of Fractional Differential Systems

Fractional calculus equations can be used to describe some phenomena and pro-cesses of many fields such as physics,chemistry,aerodynamics,electrodynamics of a complex medium,polymer rheology,capacitor theory,electrical circuits,biology,control theory,fitting of experimental data,and so on.Therefore,the study of fractional calculus equations has important theoretical significance and application value.In this thesis,the existence and multiplicity of solutions of two kinds of fractional differential equations are studied by using some fixed point theorems.The main research contents and research results of the dissertation are as follows:1.A class of nonlinear fractional-order differential coupled systems with fractional-order impulses and non-local boundary value conditions are studied(?)We study the nonlocal boundary value problem for a nonlinear fractional differen-tial coupled system with fractional order impulses.Applying Nonlinear Alternative of Leray-Schauder,we obtain some new existence results for this system.As applica-tion,an interesting example is given to illustrate the effectiveness of our main result.2.A class of higher-order Hadamard-type fractional differential equations with boundary conditions is studied(?)Using the the Guo-Krasnoselskii fixed point theorem on cone and the Leggett-Williams fixed point theorem to prove the existence and multiplicity of solutions of the higher-order Hadamard-type fractional differential equation.Examples illustrate the availability of the resulting existential theorem and the multiple theorem.The obtained results of existence and multiplicity provide theoretical support for solving fractional differential equations by fixed point theorems.