The Existence And Stability Of Solutions For Several Kinds Of Fractional Differential Equations

Fractional calculus is the expansion of the integer-order calculus theory.With research deepening,application fields of fractional differential equation continuously expanding,such as Rheology,Biophysics,Signal processing system and so on.For fractional order differential equation,it is especially important for the existence,uniqueness and stability of the solution.This thesis mainly consists of three chapters.(1)We consider two different cases of fractional integral operator the calculation of spectral radius,an example is given to illustrate the application of the conclusions.(2)Computation and analysis of the Green function for the fractional differential equation in the periodic boundary conditions,given the necessary conditions for the existence of the nontrivial solutions,we extend this conclusion to the condition that the differential equation has only zero solutions.(3)In this part,we focuses on the existence and uniqueness of solutions for the fractional differential equation with boundary value coupled systems,and the solution is Mittag-Leffler boundary.In this problem,the derivative is the Caputo fractional derivative.We transform it into equivalent integral equations,by the Bannach contraction mapping principle,we proved that the existence and uniqueness of the solution,and the solution is Mittag-Leffler boundary.