An Efficient Numerical Method for Fractional Differential Equations with Two Caputo Derivatives

Abstract

In this paper, we study the Hermite cubic spline collocation method with two parameters for solving an initial value problem (IVP) of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 ‹ β ‹ α ‹ 1 are two parameters associated with the fractional differential equations.