Infinitely many solutions to boundary value problems for a coupled system of fractional differential equations

Using the variational methods, we investigate the solutions to the boundary value problems for a coupled system of fractional order differential equations. First, we obtain the existence of at least one weak solution by the minimization result due to Mawhin and Willem. Then, the existence criteria of infinitely many solutions are established by a critical point theorem due to Rabinowitz. At last, some examples are also provided to illustrate the results.