On some generalizations of the implicit Euler method for discontinuous fractional differential equations
We discuss the numerical solution of differential equations of fractional order with discontinuous right-hand side. Problems of this kind arise, for instance, in sliding mode control. After applying a set-valued regularization, the behavior of some generalizations of the implicit Euler method is investigated. We show that the scheme in the family of fractional Adams methods possesses the same chattering-free property of the implicit Euler method in the integer case. A test problem is considered to discuss in details some implementation issues and numerical experiments are presented. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
fractional differential equation set-valued regularization fractional adams method discontinuous problem implicit method