Collocation methods for fractional differential equations involving non-singular kernel

A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed.