On the Solution of Nonlinear Fractional-Order Differential Equations
Used in the Modeling of Viscoplasticity
(with A.
D. Freed)
In F. Keil, W. Mackens, H. Voß, J. Werther (eds.):
Scientific Computing in Chemical Engineering II.
Computational Fluid Dynamics, Reaction Engineering, and
Molecular Properties.
Springer-Verlag, Heidelberg (1999),
217-224.
1991 Mathematics Subject Classification: 26A33, 65L05, 65L06, 65L70,
73E60.
Key words: Fractional differential equation, viscoplasticity,
predictor-corrector method, Riemann-Liouville derivative, Caputo derivative.
Abstract
The authors have recently developed
a mathematical model for the description of the behavior of
viscoplastic materials. The model is based on a nonlinear
differential equation of order $\beta$, where $\beta$ is a
material constant typically in the range
$0<\beta<1$. This equation is coupled with a first-order differential
equation. In the present paper, we introduce and discuss a numerical
scheme for the numerical solution of these equations.
The algorithm is based on a PECE-type approach.
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