Central Part Interpolation Approach for Solving Initial Value Problems of Systems of Linear Fractional Differential Equations

We consider an initial value problem for a system of linear fractional differential equations of Caputo type. Using an integral equation reformulation of the underlying problem, we first study the existence, uniqueness and smoothness of its exact solution. Based on the obtained results, a collocation-type method using the central part interpolation approach on the uniform grid is constructed and analyzed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.