Approximation approach to periodic BVP for mixed fractional differential systems

A numerical-analytic technique is presented for approximation of solutions of coupled fractional differential equations (FDEs) with different orders of fractional derivatives and subjected to periodic boundary conditions. Convergent sequences of functions are constructed with limit functions satisfying modified FDEs and periodic conditions. They are solutions of the given periodic BVP, if the corresponding system of determined equations has a root. An example of fractional Duffing equation is also presented to illustrate the theory.