Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Differential Inclusions: Set-Valued Maps and Viability Theory
Differential Inclusions: Set-Valued Maps and Viability Theory
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Fractional Adams-Moulton methods
Mathematics and Computers in Simulation
On some explicit Adams multistep methods for fractional differential equations
Journal of Computational and Applied Mathematics
Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
SIAM Journal on Numerical Analysis
On linear stability of predictor-corrector algorithms for fractional differential equations
International Journal of Computer Mathematics
On accurate product integration rules for linear fractional differential equations
Journal of Computational and Applied Mathematics
Generalized exponential time differencing methods for fractional order problems
Computers & Mathematics with Applications
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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.