Baffet, Daniel HenriHesthaven, Jan S.2016-04-172016-04-172016-04-17201710.1007/s10915-017-0393-zhttps://infoscience.epfl.ch/handle/20.500.14299/125731WOS:000408109600011High-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.fractional differential equationsVolterra equationskernel reductionhigh-order numerical methodsintegral deferred correctionlocal schemestext::journal::journal article::research article