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Explicit methods for fractional differential equations and their stability properties. (English) Zbl 1169.65121
The authors investigate a class of multistep methods for fractional differential equations and study the stability. A formula for the region of stability of the methods under investigation is obtained. The stability of some existing explicit methods is also studied. The authors derive new methods of the first and second order with interval of stability and provide numerical examples to illustrate the methods discussed.

MSC:
65R20 Numerical methods for integral equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
26A33 Fractional derivatives and integrals
45J05 Integro-ordinary differential equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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