Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Automatic Computations with Power Series
Journal of the ACM (JACM)
Pitfalls in fast numerical solvers for fractional differential equations
Journal of Computational and Applied Mathematics
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
On some explicit Adams multistep methods for fractional differential equations
Journal of Computational and Applied Mathematics
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
A new stochastic approach for solution of Riccati differential equation of fractional order
Annals of Mathematics and Artificial Intelligence
Quadratic spline solution for boundary value problem of fractional order
Numerical Algorithms
A family of Adams exponential integrators for fractional linear systems
Computers & Mathematics with Applications
Mathematics and Computers in Simulation
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In the simulation of dynamical systems exhibiting an ultraslow decay, differential equations of fractional order have been successfully proposed. In this paper we consider the problem of numerically solving fractional differential equations by means of a generalization of k-step Adams-Moulton multistep methods. Our investigation is focused on stability properties and we determine intervals for the fractional order for which methods are at least A(@p/2)-stable. Moreover we prove the A-stable character of k-step methods for k=0 and k=1.