Qualitative Analysis Of Several Types Of Katugampola Fractional Differential Equations

In 2011,Katugampola presented a new definition of fractional integral,which generalizes the Riemann-Liouville and Hadamard integral into a single form.In 2014,He came up with the corresponding definition of fractional derivative called Katugampola derivative.In this paper,we mainly study the qualitative analysis of several kinds of Katugampola fractional differential equations,as follows:Chapter one,briefly introduces the basic knowledge and the background of the research.Chapter two,by using both Banach fixed point theorem and Schauder fixed point theorem,we study that under nonlocal conditions whether the existence and uniqueness of solutions exist for a kind of the Katugampola fractional differential equation.Chapter three,by using Schauder fixed point theorem,we study the attraction of solutions for a kind of the Katugampola fractional differential equation.Chapter four,by using successive approximation,we study that under nonlocal conditions whether the existence and uniqueness of solutions exist for a kind of the fuzzy differential equation in Hilfer-Katugampola fractional derivative.Chapter five,the summary of this thesis.