| Caputo-katugampola type fractional calculus has developed rapidly with the research of fractional calculus theory and application.According to the published papers,the research on this type of differential system mainly focuses on the existence and uniqueness of the solutions.In this paper,we study the existence and uniqueness of solutions and asymptotic stability of several types of caputo-katugampola nonlinear fractional differential systems.First,we study the existence and uniqueness of positive solutions to nonlinear fractional-order boundary value problems with order ∈(2,3)In the Banach space,by the cone expansion and compression fixed point theorem,the existence of the positive solutions were testified.The uniqueness of the positive solutions were proved by the Banach fixed point theorem.then,we discuss the existence and uniqueness of the solutions of fractional differential equations of type caputo-katugampola and proves the asymptotic stability of the zero solutions of the differential equations.In this paper,some properties of Caputo type fractional order differential are extended to Caputo-Katugampola type fractional order differential,and positive integer order Lyapunov function is constructed by this method to obtain the asymptotic stability of this fractional order non-autonomous system.Finally,we study the existence and uniqueness of solutions for caputo-katugampola type coupling system.In Banach space,leray-schauder’s alternative is used to prove the existence of the solution of the system,and the uniqueness of the solution is proved by Banach fixed point theorem. |
