Solvability For Several Classes Of Fractional Coupled Systems

In this paper,the solvability of three kinds of fractional coupled systems is studied.According to the characteristics of the studied systems,the appropriate fractional derivative space is selected and the corresponding variational functional of the system is constructed.We transform the existence and multiplicity of solu-tions of the fractional coupled systems into the existence and multiplicity of the critical point of the corresponding functional.After constructing the variational functional,and based on the very recent three critical points theorem and the general variational principle,we provide some sufficient conditions for the exis-tence of solutions to the boundary value problems of these three kinds of fractional coupled systems.The results obtained in this thesis extend some existing results on the solvability of integral order coupled systems to fractional coupled systems and extend the application of variational methods in studying the solvability of fractional coupled systems.