On Application of the Contraction Principle to Solve the Two-Term Fractional Differential Equations

We solve two-term fractional differential equations with left-sided Caputo derivatives. Existence-uniqueness theorems are proved using newly-introduced equivalent norms/metric on the space of continuous functions. The metrics are modified in such a way that the space of continuous functions is complete and the Banach theorem on a fixed point can be applied. It appears that the general solution is generated by the stationary function of the highest order derivative and exists in an arbitrary interval [0,b].