High-Order Adaptive Methods for Fractional Differential Equations Using a Reduced Kernel Formulation
High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our study on 1-step methods and approximate the local part of the fractional integral by integral deferred correction to enable high order accuracy. We present numerical results obtained with both implicit and the explicit methods applied to different problems.