| In 2015,Caputo and Fabrizio proposed a definition of fractional derivative with smooth kernel,called the Caputo-Fabrizio derivative.In this thesis,the solvability of several classes of fractional differential systems with Caputo-Fabrizio derivative are studied.In the first part,we use Banach contraction mapping principle and Leray Schauder nonlinear alternative to study the existence and uniqueness of solutions for a system of fractional differential equations with boundary value conditions.In the second part,we use Schauder fixed point theorem and Banach contraction mapping principle to study the existence and uniqueness of solutions for the initial value problem of a system of fractional differential equations.In the third part,we use Banach contraction mapping principle to study the existence and uniqueness of solutions for the initial value problem of a system of fractional differential equations with variable order.Finally,we provide corresponding example for each chapter to demonstrate the applicability of the theorem. |
